BIBLIOGRAPHY ON THE COMPLETELY DECOMPOSED

TOPOLOGY AND ITS APPLICATIONS

We list below the works where the completely decomposed topology (or as it iscommonly called now the Nisnevich topology) and various related structures and con-structions have been introduced and developed, as well as the papers where theseconstructions and the results based on them have been used in a variety of contexts.The order of sections and the order of papers inside of each section are chronological.

TABLE OF CONTENT

I. Monographs and surveys, pp. 2 - 8.

II. Papers, pp. 8 - 60.

1. The basic constructions, p. 8.

2. Applications to the structure, arithmetic and cohomology of algebraic groups,pp. 8 - 13.

3. Applications to the higher dimensional class field theory, p. 13-15.

4. Applications to the Algebraic K-theory, pp. 15-22.

5. Applications to a study of algebraic cycles, their intersections and the Picard andHigher Chow groups, pp. 22-25.

6. Applications to the Theory of Motives and Motivic Cohomology, pp. 25 - 38.

7. Applications to motivic homotopy theories of algebraic varieties and schemes,pp. 38 - 54.

8. Applications to other classes of cohomology theories, pp. 54-57.

9. Applications to derived and non-commutative algebraic geometry and stacks, pp.57-58.

10. Some other applications and connections, pp. 58-59.

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I. MONOGRAPHS, SURVEYS AND LECTURE NOTES

1. Ye. Nisnevich, Etale Cohomology and arithmetic of semisimple groups, HarvardThesis, 1982.

2. Ye. Nisnevich, The Completely Decomposed Topology and its Applications. ASurvey, Preprint, 1992, pp. 1-71.

3. K. Kato, Generalized Class Field Theory, in: ”Proceedings of the Inter-national Congress of Mathematicians, Kyoto, Japan, 1990”, Invited talk,v.1, pp. 381-394, Berlin, Springer Verlag, 1992 (ed. I. Satake); http ://www.mathunion.org/ICM/ICM1990.1/Main/icm1990.1.0419.0428.ocr.pdf .

4. R. W. Thomason, A local to global principle in the Algebraic K-theory, Proceed-ings of the Internat. Congress of Mathematicians, Kyoto, Japan, 1990, Invitedtalk, v.1, pp. 419-428, Berlin, Springer Verlag, 1992 (ed. I. Satake); http ://www.mathunion.org/ICM/ICM1990.1/Main/icm1990.1.0381.0394.ocr.pdf .

5. W. Raskind, Abelian Class Field Theory of arithmetic schemes, in: Algebraic K-theory and Algebraic Geometry: Connections with Quadratic Forms and DivisionAlgebras, Proc. Symp. Pure Math., v. 58, part 1, A.M.S., Providence, 1994, pp.85-187.

6. A. A. Suslin, Algebraic K-theory and motivic cohomology, Proc. Inter-nat. Congress of Math., Aug. 1994, Zurich, Invited talks, v. 1,pp. 342-351, Birkhauser, 1996, www.mathunion.org/ICM/ICM1994.1/Main/icm1994.1.0342.0351.ocr.pdf ; see also Zbl 0841.19002.

7. J. R. Jardine, Generalized etale cohomology theories, Progress in Mathematics, v.146, Birkhauser, 1997, 328pp; 2nd ed.: Modern Birkhauser classics (paperback),2011, 60 Eu.

8. S. Bloch, Lecture on Mixed Motives, Proceeding of the Amer. Math. Soc. Sum-mer Reserch Institute on Algebraic Geometry, Santa Cruz, 1995, Proc. Sympos.in Pure Math., v. 62, Part 1, AMS, Providence, 1998, pp. 329-359; see alsohttp : //www.math.uchicago.edu/motive.ps

9. E. M. Friedlander, Motivic complexes of Suslin-Voevodsky, Seminaire Bourbaki,t. 49 (1996/97), expose 833/01-20, Juin 1997, Asterisque, t. 245 (1998), pp.355-378; see also http : //www.numdam.org/ARCHIV E/SB... reprinted inthe Handbook of K-theory (see item I-39 below), pp. 1081-1104.

10. B. Kahn, La Conjecture de Milnor (d’apres V. Voevodsky), SeminaireBourbaki, 49 (1996/97, expose 834/01-40, Juin 1997, Asterisque, t. 245(1998), 379-418; http : //www.nundam.org/ARCHIV E/SB/ or http ://www.math.jussieu.fr/ ∼ kahn/...or http : //www.math.uiuc.edu/K −

theory, no. 210; reprinted in the Handbook of K-theory (see item I-39 below),pp. 1105-1149.

11. M. Levin, Mixed Motives, Mathematical surveys and monographs, v. 57, AMS,

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Providence, 1998, 518pp.

12. F. Morel, Voevodsky’s proof of Milnor’s Conjecture, Bull. A.M.S., v. 35 (1998),No. 2, pp. 123-143.

13. V. Voevodsky, A1-Homotopy theory, Proc. Intenat. Congress Mathemat., Berlin,1998, Plenary talk, Documenta Math., Extra Vol.: ICM 1998, vol. 1, pp. 579-604.

14. V. Voevodsky, A. Suslin, E. Friedlander, ”Cycles, Transfers and Motivic Homol-ogy Theories”, Annals of Math. Studies, v. 143, Princeton Univ. Press, 2000,pp. 1-260; see also http : //www.math.uiuc.edu/K − theory, no. 368.

15. F. Morel, Theorie homotopique des schemas, Asterisque, t. 256, Soc. Math.de France, 1999, 130pp; English translation: Homotopy theory of schemes,SMF/AMS Texts and Monographs, v. 12, Paris, 2006, 112pp; Introduction:http : //www.mathaware.org/bookstore/pspdf/smfams − 12 − intro.pdf .

16. A. Suslin, Voevodsky’s proof of the Milnor Conjecture, in: Current developmentsin Mathematics, 1997, pp. 173-188, Internat. Press, Boston, MA, 1999, eds.Bott R., Jaffe A., Yau S.-T., Jerisson D., Luzstig G., Singer I.

17. V. Voevodsky, Seattle Lectures: K-theory and Motivic Cohomology, in: AlgebraicK-theory, Proc. Symp. in Pure Math., v. 67, AMS, Providence, 1999, pp. 183-203; see also http : //www.math.uiuc.edu/K − theory, no. 316.

18. C. Mazza, V. Voevodsky, Ch. Weibel, Lecture Notes on Motivic Cohomol-ogy, series Clay Mathematics Monographs, no. 2, Amer. Math. Soc., Prov-idence, 2006, 210pp.; see also http : //www.math.rutgers.edu/ ∼ weibel/MV WNotes/prova − hyperlink.pdf .

19. V. Voevodsky, Lectures on Motivic Cohomology, IAS, 2000/2001, (notes writ-ten by P. Deligne), in: Algebraic Topology, The Abel Symposium 2007, AbelSymposia ser., v. 4, eds. N. Baas, E. Friedlander, P.-A. Ostvaer, Springer,2009, pp. 355-409, www.springerlink.com/index/u15802237j968222.pdf ; seealso http : //www.math.uiuc.edu/K − theory, no. 527, 2001, pp. 1-65; orarXiv:0805.4436v1, [math.AG], pp. 1-64, 28 May, 2008.

20. S. Mueller-Stach, Algebraic cycle complexes, Basic properties, Proc. Conf. Ban-iff, 2001?, pp. 1-22, available at http : //hodge.mathematik.uni − mainz.de/ ∼

stefan/papers/baniff.pdf

21. J. Riou, Theorie homotopique des S-schemas, Memoire DEA, Ecole NormaleSuperieure, Paris, 2001, pp. 1 - 105, http : //www.eleves.ens.fr : 8080/home/jriou.

22. F. Morel, An introduction to A1-homotopy theory, in: Contemporary develop-ment in Algebraic K-theory, International Center for Theoretical Physics, Trieste,Lecture Notices, v. 15 (2003), M. Karoubi, A. Kuku, C. Pedrini (eds.), Trieste,pp. 357-441, see also http : //www.mathematik.uni − muenchen.de/ ∼ morel.

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23. J. F. Jardine, Generalized sheaf cohomology theories, in: Axiomatic, enrichedand motivic homotopy theory, NATO Advanced Study Institute Series, ser. II,Math. Physics, Chemistry, v. 131, Elsevier Sci. Publ., 2003, J. P. C. Greenlees(ed.), pp. 29-68; see also http : //www.newton.ac.uk/preprint/NI02034.pdf

24. E. Friedlander, A. Suslin, The work of Vladimir Voevodsky. in The mathematicalwork of the 2002 Fields Medalists, Notes of the AMS, vol. 50 (2002), no. 2, pp.214-216.

25. V. Voevodsky, Open problems in the motivic stable homotopy theory I, in: FieldsMedalists’ Lectures, M. Atiyah and D. Iagolnitzer (eds.), 2nd ed., World Sci. Ser.on 20th Century Math., v. 9, 2003, World Sci., 2003, pp. 781-815.

26. P. Hu, S-modules in the category of schemes, Memoirs of the AMS, v. 161, no.767, 2003, 134pp; see also http : //www.math.uiuc.edu/K − theory, no. 396.

27. Y. Takeda, On the Voevodsky’s construction of the cateory of mixed motives,Sugaku, v. 53(2001), no. 1, pp. 1-17; English translation: Sugaku Expositions,v. 16 (2003), no. 2, pp. 207-224.

28. M. Chalupnik, A. Weber, Motywy Vladimira Voevodskiego, Wiadomosci Matem-atyczne, vol. 39 (2003), pp. 27-38; see also http : //www.mimuw.edu.pl/ ∼

aweber/publ.html

29. C. Mazza, On Voevodsky’s work, in: Symposium on Algebraic geometry at Hi-rosima, Preprint, 2003, pp. 1-65, available at http : //www.math.sci.hirosima−u.ac.jp/algebra/agsympo/documents/sem.pdf .

30. E. Friedlander, Motives and K-theory, Lectures at the ETH, Zurich, Winter of2003/04 (7 lectures), available at http : //www.math.nwu.edu/ ∼ eric/lectures

31. E. Friedlander, Cohomology and K-theory, Lectures at the InstituteHenri Poincare, Paris, Spring, 2004 (6 lectures), available at http ://www.math.nwu.edu/ ∼ eric/lectures.

32. Motives, homotopy theory of varieties and dessins d’enfants, Workshop at theAmerican Institute of Mathematics, Palo Alto, CA, April, 2004, pp. 1-22, avail-able at http : //www.aimath.org/WWN/motivesdessins/motivic/pdf .

33. Motives and Homotopy theory of schemes, Arbeitsgemeinschaft mit aktuellenThema, Organized by T. Geisser, B. Kahn and F. Morel, MathematischesForschungsinstitut Oberwolfach, Oberwolfach Reports, v.1 (2004), No. 2, pp.785-827, available at http : //www.mfo.de/programme/schedule/2004/12/OWR 2004 15.pdf .

34. Y. Andre, Une introduction aux motifs (Motifs purs, motifs mixtes, periodes),Panaramas et synthesis, t. 17, Soc. Math. de France, Paris, 2004, 275pp.

35. J. F. Jardine, Lectures on presheaves of spectra, Univ. of Western Ontario, FallSemester of 2005/06, 10 lectures. available at http : //www.math.uwo.ca/ ∼

jardine/papers/Spt/index.shtml.

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36. J. F. Jardine, Lectures on simplicial presheaves, Univ. of Western Ontario,Winter Semester of 2004/05, 15 lectures, available at the K-theory archive,http : //www.math.uiuc.edu/K − theory, no. 735.

37. M. Hopkins, Lecture cours on Motivic Homotopy theory, Harvard, Fall 2004, 8lectures, available at http : //www−math.mit.edu/ ∼ tlawson/motivic.html orhttp : //www.math.umn.edu/ ∼ tlawson/motivic.html.

38. A. Schmidt, Higher dimensional class field theory (from a topological point ofview), Preprint, 2005, pp. 1-12, available at http : //www.mathematik.uni −regensburg.de/Forschergruppe/Preprints/2005/01 − 2005.pdf , or http ://repository.kulib.kyoto − u.ac.ukjp/dspace/handle/2433/47732.

39. L. Barbieri-Viale, A pamphlet on Motivic Cohomology, Milano J. of Math., 73(2005), 53-73; see also http : //www.math.unipd.it/ barbieri/MJH.pdf .

40. Handbook of K-theory, vv. 1,2, eds. E. Friedlander and D. Grayson, Springer,2005.

41. M. Kashiwara and P. Schapira, Caterories and Sheaves, Die Grundlehren derMathematishen Wissenschaften, b. 332, Springer, 2006, 507pp., see especiallychapters:

Ch. 16: Grothendieck Topologies: http : //www.springerlink.com/index/k6r3r86j304278h0.pdf

Ch. 17: Sheaves on Grothendieck Topologies: http : //www.springerlink.com//index/x5732537121h7304.pdf

42. A. Beilinson, V. Vologodsky, A DG guide to Voevodsky motives, Geom.Anal. Funct. Anal., v. 17 (2008), pp. 1709-1787; see also http ://www.math.uiuc.edu/K − theory, no. 820??, http : //www.arXiv.org, no.math.AG/0604004, v.5, June, 2008.

43. M. Levine, Six Lectures on Motives, Ecole d’iete France- Asiatique de GeometrieAlgebrique et Theorie des Numbres 2006, ”Autour de Motifs”, IHES, July, 2006,http : //www.ihes.fr/IHES/scientifique/asie/textes.

44. Algebraic K-theory, Organized by D. Grayson, A. Huber-Klawitter, UweJannsen, Marc Levine, July 16-22, 2006, Mathematisches Forschungsin-stitut Oberwolfach, report 32/2006, available at http : //www.mfo.de/programme/schedule/ 2006/29/OWR 2006.32.pdf .

45. F. Morel, A1-algebraic topology, in: Proc. Internat. Congress ofMathemat. (ICM), Madrid, Spain, Aug. 2006, invited talks, v. 2,pp. 1035-59, Europ. Math. Soc., Zurich; available at http ://www.ism2006.org/proceedings/V ol II/contents/ICM V ol2 49.pdf ;

46. Sedano Winter School on K-theory, 2007, pp. 1-66, available athttp : //cmj.dw.uba.ar/Members/gcorti/workgroupswick/en/sedam.pdf ; in-cludes C. Mazza, Voevodsky motives and K-theory, pp. 1-66, http :

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//cms.dm.uba.ar/Members/gcorti/workgroup.swisk/sem.pdf

47. 2nd Workshop on Motives, Univ. Tokyo, Sept. 25-29, 2006, available athttp : //www.ms.u − tokyo.ac.uk.jp/ ∼ gokun/document/Motives − 2nd −

LectureNotes − All.pdf , pp. 1-110.

48. Algebraic Cycles and Motives, Proc. of the EAGER Conf. held in Leiden, Aug.30- Sept. 4, 2004, in a Honor of the 75th anniversary of J. P. Moore, vols. 1, 2,eds. J. Nagel, C. Peters, London Math. Society Lecture Notes Series, CambridgeUniv. Press, vols. 343, 344, 2007 (Ayoub J., Barbieri-Viale L., Deglise F., KahnB., Moore J. P.).

49. B. Dundas, M. Levine, P. A. Ostvaer, O. Rondigs, V. Voevodsky, Motivic Ho-motopy Theory, Lectures at the Summer School in Nordjordeid, Norway, Aug.2002, Berlin, Springer, ser. Universitext, Feb., 2007, 228pp.

Ch. II, pp. 115-145, Sheaves for a Grothendieck Topology, available at http ://www.springerlink.com/content/r2113827j72i76m2/fulltext.pdf .

Ch. III, pp. 147-225, Voevodsky’s Nordfjordeid Lectures, Motivic ho-motopy, by V. Voevodsky, O. Roendigs, P. A. Ostvaer, available at http ://www.springerlink.com/content/w43142212281r1q3/fulltext.pdf

Ch. IV, pp. 227-240, Motivic spectra, by I. Dundas, available at http ://www.springerlink.com/content/1107/q51825185597/fulltext.pdf

50. B. Klingler, Introduction aux motifs de Voevodsky, Une approche geometrique,Cours de M2 donne a Institut de Mathematique de Jussieu, 2006. Notesredigees par Benjamin Collas et Ismael Souderes, pp. 1-52, version du 23Mai, 2007 (incomplete), available at http : //people.institut.math.jussieu.fr/ ∼

collas/math/Klingler − IntroductionMotifs − coursM2.pdf .

51. Algebraic K-theory and Trieste, May, 2007, ICTP Lecture Notice ser., v. 23,435pp, eds. E. Friedlander, O. Kuku (U. Iowa), C. Pedrini, Trieste 2008; freeaccess via: http : //www.ictp.it/pages/organization/publications.html or http ://publications.icth.it/lns.html

(main relevant lectures: E. Friedlander, M. Levine, C. Weibel)

52. E. Friedlander, Lectures on algebraic K-theory and motives at ICTP, July 2007(6 lectures), pp. 1-77, see item I-49 above.

53. M. Levine, Lectures on Mixed Motives at ICTP, 2007 (6 lectures), see item I-49above, notices also available at http : //www.math.neu.edu/ ∼ levine/pubs/,pp. 139-226.

54. C. Weibel, Lectures on Bloch-Kato conjecture at ICTP (6 lectures), see item I-49above, notices also available at http : //www.math.rutgers.edu/ ∼ weibel, pp.281-305.

55. F. Ivorra, Petite introduction aux motifs, Lectures, Univ. Rennes I, Dec.2007, pp. 1-30, available at http : //perso.univ − rennes1.fr/xavier.caruso/

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seminterne/ivorra0708.pdf .

56. M. Levine, Three lectures on motives and motivic cohomology, Conference onMotives, quantum field theory and pseudodifferential operators, June, 2008, no-tices avilablea at http : //www.math.neu.edu/ ∼ levine/pubs.

57. M. Levine, Motivic homotopy theory, Milan Journal of Mathematics, v. 76(2008), no. 1, pp. 165-199, see also http : //www.springerlink.com/content/6232541085753086/.

58. S. Bloch, Motivic cohomology, in ”Aspects de Geometrie Algebrique: la pos-terite mathematique de Grothendieck, IHES, Jan. 9-14, 2009, available athttp : //www.math.uchicago.edu/ ∼ Bloch/talk090108, pp. 1-18.

59. V. P. Snaith, Stable homotopy theory around the Arf-Kervaire invariant, Progressin Math., v. 273 (2009), 220pp.Ch. 17. Futuristic and contemporary stable homotopy theory, pp. 199-215;http : //www.springerlink.com/index/vq611501271225ul.pdf .

60. J. Lurie, Higher topos theory, Princeton U. Press, Annals of Math. Studies, 2009,925pp.

61. J. F. Jardine, Lectures on local homotopy theory, Univ. of Western Ontario,Spring 2009 and 2010, 14 lectures, http : //www.math.uwo.ca/ ∼ jardine.

62. D. Asok, Ideas of geometric topology in algebraic geometry or geometric appli-cations of A1-homotopy theory, a lecture, Brown U., March 6, 2009, pp. 1-64,www.math.brown.edu/ ∼ abramovic/AsokSponsorsTalk.pdf

63. Algebraic Topology, Abel Symposium. 2007, in the series ”Abel Symposia”, v. 4,eds. N. Baas, E. Friedlander, P. A. Ostvaer, Springer, 2009; the relevant entries:1) Panin-Pimenov-Roendigs, see item II, §7-127 below; 2) Voevodsky, see itemI-19 above. See also unpublished lecture notes by H. Esnault and M. Levine,available at http : //www.abelsymposium.no/2007.

64. F. Deglise, Complexes Motiviques (d’apres Voevodsky), a course of 13 lectures,Institut Galelee, Univ. Paris 13, Oct. 2009 - Feb. 2010, http : //www.math.u −

paris13.fr/ deglise/cours.html.

65. Bloch S., Lectures on algebraic cycles, 2nd ed., New mathematical monographs,Cambridge Univ. Press, 2010, http : //assets.cambridge.org/97805211/18422/frontmatter/970521118422 frontmatter.pdf .

66. Descente cohomologique, localization et constructibilite dans les categories mo-tiviques, Groupe de travaile a l’Univ. Paris 13, 2010 (Cisinski Ch., Deglise F.,Drew B., Kelley S., Pepin-Lalleur S.), Printemps 2010, exposes I - XV, availableat http : //www.math.univ − paris13.fr/ ∼ kelly.

67. S. Saito, Cohomological Hasse principle and motivic cohomology Proc. Int.Congr. Math., 2010, Haidarabad, India (to appear), pp. 1-26, available atwww.lcv.ne.jp/ ∼ smaki/en/articles/icm − total.pdf

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68. J. F. Jardine, Local homotopy theory, a book in preparation, July 2012, pp.1-283, http : //www.math.uwo.edu/ ∼ jardine/papers/preprints/book.pdf ,1300Kb.

69. F. Morel, A1-algebraic topology over a field, Lect. Notes in Math.,v. 2052, pp. 1-296 (to appear 2012); an earlier version in http ://hopf.math.purdue.edu/Morel/A1homotopy.txt, pp. 1-126, Nov. 2006.

70. Motives and Milnor conjecture, Ecole d’ete, Institut de mathematique de Jussieu,Paris, Juin 9-17, 2011, Organisateurs: F. Deglise. V. Maillot, J. Wildehause,http : //motives − 2011.institut.math.jussieu.fr/notes/.

71. Articles on categorical logics, including Grothendieck topology, 2011,www.amazon.fr/Articles-Categorical-Logic-...

72. Motivic integrastion and its interaction with model theory and motives. eds.Cluckers/Nicaise/Sebag, 2012.

73. J. Lurie, Derived algebraic geometry, Ch. I-XIV, 2011-2012, http ://www.math.harvard.edu/ ∼ lurie/papers/DAGx.pdf , x = I, II,...,,XIV; see§II.9 below for more details.

74. Luc Illusie, Yves Lasclo, Fabrice Orgogozo, Travaux de Gabber surl’uniformization locale et la cohomologie etale des schemas quasi-excelents.Seminaire a l’Ecole polytechnique 2006-2008 (2012), arXiv:1207.3648, [math.AG],pp. 1-416??, July 2012.

75. P. Herrmann, Equivariant motivic homotopy theory and motivic Borel cohomol-ogy, Dissertation, Univ. Osnabruck, June 2012.

76. Regulators: Regulators III, Proc. Conf. Barcelona, July 12-22, 2010, ed. J. I.Burgos, 270pp, 2013,

77. C. Weibel, The K-book, Introduction to algebraic K-theory, AMS, 2013, 618pp.

78. J. Moore, Jim Nagel, Ch. Peters, Lectures on the theory of pure motives, 2013,149pp.

II. PAPERS

1. THE BASIC CONSTRUCTIONS.

1. Ye. Nisnevich, Arithmetical and cohomological invariants of semisimple groupschemes and of compactifications of locally symmetric spaces, Functional Analysisand its Applications, v. 14 (1980), pp. 61-62.

2. Ye. Nisnevich, Adeles and Grothendieck topologies, Ch. I of the Harvard Thesis,1982, pp. 1-35, see title I.1, see also http : //www.cims.nyu.edu/ nisnevic.

3. Ye. Nisnevich, The completely decomposed topology on schemes and associated

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spectral sequences in the Algebraic K-theory, in: ”Algebraic K-theory: Connec-tions with Geometry and Topology”, J. F. Jardine and V. Snaith (editors), NATOAdvanced Study Institute Series, Ser. C, v.279, Kluwer,1989, pp. 241-342.

4. Anel M., Grothendick topologies from unique factorization systems, availableat http : //crm.es/Publications/09/Pr847.pdf , pp. 1-67; see also http ://thales.math.uqam.ca/ ∼ anelm/mat/doc/factorization.pdf .

5. F. Deglise. Introduction a la topologie de Nisnevich, Preprint, 1999, pp. 1-20,http : //www.math.univ − paris13.fr/ ∼ deglise/docs/avant2000.

6. M. Hoyois, Notes on the Nisnevich topology and Thome spaces in mo-tivic homotopy theory, with a proof of the motivic tubular neighborhoodtheorem, Preprint, 2010, pp. 1-16, http : //www.northwestern.edu/ ∼

hoyois/papers/nisnevich.pdf .

2. APPLICATIONS TO THE STRUCTURE, ARITHMETIC

AND COHOMOLOGY OF ALGEBRAIC GROUPS

1. Ye. Nisnevich, 1980, see item II.1.1. above.

2. Ye. Nisnevich, 1982, see item II.1.2 above.

3. Ye. Nisnevich, Espaces homogenes principaux rationnellement triviaux etarithmetique des schemas en groupes reductifs sur les anneaux de Dedekind,Comptes Rendus Academie des Sciences, Paris, t. 299 (1984), No. 1, pp. 5-8.

4. Ye. Nisnevich, On certain arithmetic and cohomological invariants of semisimplegroups, Preprint, 1988, pp. 1-44.

5. Ye. Nisnevich, Generalized integral Iwasawa and Bruhat- Steinberg decompo-sitions for semisimple group schemes over Dedekind rings, Preprint, 1988, pp.1-46.

6. Ye. Nisnevich, On the Serre - Grothendieck Conjecture concerning rationallytrivial principal homogeneous spaces, Preprint, 1988, 1-90.

7. Ye. Nisnevich, Espaces homogenes principaux rationnellement triviaux, pureteet arithmetique des schemas en groupes reductifs sur les extensions des anneauxlocaux reguliers de dimension 2, Comptes Rendus Acad. Sciences, Paris, t. 309(1989), No. 10, pp. 651-655.

8. J. Rolf, B. Speh, Representations with cohomology in the discrete spectrum ofarithmetic subgroups of SL(n,1), Annales Sci. Ecole Norm. Super., t. 20 (1987),No.1, 89-136.

9. J.-L. Colliot-Thelene, J. J. Sansuk, Principal homogeneous spaces under flasquetori- Applications, J. Algebra, v. 106 (1987), 148-205.

10. M. Morishita, On S-class number relations for algebraic tori in Galois extensions

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of global fields, Nagoya Math. Journ., v. 124 (1991), 131-143.

11. C. Douai, Points rationnelles dans les espaces homogenes des groupes semi-simplesur les anneaux de Dedekind, Publ. Inst. Math. Avancee, Lille, 1992, v. 28, No.IV, pp. 1-17.

12. J.-C. Douai, Espaces homogenes rationnallement triviaux et arithmetique desschemas en groupes reductifs sur anneau de Dedekind. Comptes Rendus deAcad. Sciences, Paris, t. 317(1993), pp. 1007 - 1012.

13. P. Gille, Torseurs sur la droit affine et R-equivalence, Thesis, Orsay, 1994?, avail-able at http : //www.math.u − psud.fr/ ∼ gille/prepublis/doct.pdf ; cat.inist.fr

14. J.-C. Douai, Espaces homogenes et arithmetique des schemas en groupes reductifssur les anneaux de Dedekind, Journ. de Theorie des Nombres de Bordeaux, 7(1995), 21-26

15. P. Gille, R-equivalence and Norm Principle in Galois Cohomology, Comptes Ren-dus Acad. Sciences, Paris, t. 316(1993), pp. 315-320.

16. B. Mazur, On the passage from local to global in the Number Theory, Bull. ofthe Amer. Math. Society, 29(1993), No. 1, pp. 14-50.

17. Thang NG, On some new Local to Global Principles over a Real Function Field,Comm. in Algebra, 22 (1994), no. 6, 2205-2219.

18. Thang NG, Some local to global principles in arithmetic of alg. groups over realfunction fields, Math. Zeit. 221 (1996), pp. 1-19.

19. J.- L. Colliot Thelene, M. Ojanguren, Locally trivial homogeneous spaces, Publ.Math. IHES, 75 (1992), 97-122.

20. P. Gille, La R-equivalence sur les groupes algebriques reductifs, Publ.Math.IHES, no. 86 (1997), pp. 199-235.

21. A. Pianzola, Affine Kac-Moody Lie algebras and torsors over the puncturedline, Preprint, 2002, pp. 1-8, available at http : //www.arXiv.org/, no.math.RT/0203277.

22. K. Zainulin, Hyposis of Grothendieck for principle homogeneous spacesfor some algebraic groups, Thesis, LOMI, St. Petersburg, 2001, http ://www.mathematik.uni − bielefeld.de/ ∼ kirill/publ/thesis/phd − thesis.pdf

23. P. Gille, Torseurs sur la droite affine, Transformation groups, v. 7, no. 3 (2002),pp. 231-245,

24. I. Panin, Purity for similarity factors, in ”Algebra and number theory, Proc.of the silver jubilee conf. Univ, Hyderabad, Dec. 2003, ed. Tandon R.,pp. 66-89, Hundistan books, Dehli, 2005; see also E-print, Sept. 2003,http : //www.arXiv.org, math.AG/0309054, pp. 1-21.

25. M. Florence, Points rationnelles sur les espaces homogenes et leurs compacti-

10

fications, Transformation groups, v. 11 (2006), no. 2, pp. 161-176. see alsohttp : //www.math.uni − bielefeld.de/LAG/man/174.pdf

26. I. Panin, A purity theorem for linear algebraic groups, Preprint, 2005, pp. 1-25,available at the K-theory archive, http : //www.math.uiuc.edu/K − theory, no.729.

27. P. Gille, L. Moret-Bailly, Actions algebrique de groupes arithmetiques, Appendixto the paper Ulmo, D. Yafaev, Galois orbits of special subvarieties of Shimura va-rieties, Preprint, 2005, pp. 1-10, available at http : //www.math.u− psud.fr/ ∼

ullmo

28. Nguen Quoc Thang, Corestriction peinciple for non-abelian cohomology of re-ductive group schemes over arithmetic rings, Proc. Japan Acad. Sci., ser. A,Math. Sci. 82(2006), no. 9, pp. 147-151.

29. N. Naumann, Arithmetically defined subgroups of Morava stabilizer algebras,Composit. Math., v. 144 (2008), pp. 247-270; see also Preprint, pp. 1-28, 2006?,http : //www.tux1.nyc.aps.org

30. N. Naumann, Torsors under smooth group schemes and Morava stabilizer groups,Preprint, pp. 1-29, http : //www.math.uiuc.edu/ ganter/talbot/qiso2.pdf

31. C. D. Gonzales-Aviles, Chevalley’s ambiguous class number formulafor an arbitrary torus, Math. Res. Lett., 15(2008), 1149-1165;www.mathjournals.org/mri/2008-015-006/2008-015-006-007.pdf; an erlier ver-sion: http : //www.arXiv.org, No. 0711.1623v1, [math.NT], pp. 1-10.

32. J.-L. Colliot-Thelene, Fei Xu, Brauer-Manin obstruction for integral points ofhomogeneous spaces and representations by integral quadratic forms, E-print,http : //www.arxiv.org, no arXiv:0712.1957v1 [math.NT], 12 Dec. 2007, pp.1-54.

33. Nguen Quoc Thang, Correstriction Principle for non-abelian cohomology of re-ductive group schemes over Dedekind rings of intergers of local and globalfields, Preprint, Max Plank Institute, 2007, pp. 1-49, available at http ://www.mpim − bonn.mpg.de/preprints/send?bid = 3210

34. J. Wildeshaus, On the boundary motive of a Shimura variety, Compositio Math.143(2007), no. 4, pp. 959-985. see also http : //math.uiuc.edu/K − theory, no.708 or http : //www.arXiv.org , math.AG/0409400, pp. 1-38.

35. J. Wildeshaus, On the boundary motive of a Shimura variety, lecture at theLumini Center, Univ. Marcelle, 2007, available at http : //www.cirm.univ −

mrs.fr/videos/2007/exposes/39/wildeshaus0409400.pdf .

35. S. Gille, The first Suslin homology group of split simply connected semisimplealgebraic group, Jour. of algebra, v. 333(2011), no. 1, pp. 26-39.

36. S. Gille, The first Zariski cohomology of the first Witt sheaf over a split sim-ply connected simple algebraic group, in: ”Quadratic forms Algebra, Arith-

11

metic and Geometry”, R. Baeza, Wu Kin Chan, D. Hoffmann, R. Schulze-Pillot (eds.) Contemporary Math., v. 493, 2009, pp. 163-179; see alsohttp : //www.math.lmu.de/ ∼ gille/CohWittsheaf/pdf .

37. M. Wendt, Rationally trivial torsors in A1-homotopy theory, Preprint,November, 2008, pp. 1-29, available at http : //home.mathematik.uni −

freiburg.de/arithmetische − geometrie//preprints/wendt − fibseq.pdf.

38. M. Wendt, Homotopy invariance for homology of linear groups, Preprint, De-cember, 2008, pp. 1-??, http : //home.mathematik.uni −

freiburg.de/arithmetishce − geometrie/preprints/wendt − hoinv.pdf .

39. M. Wendt, Stabilization in Algebraic K-theory and group homology,Preprint, Dec. 2008, pp. 1-19, http : //home.mathematik.uni −

freiburg.de/arithmetische − geometrie/preprints/wendt−??.

40. N. Semenov, Motivic construction of cohomological invariants, E-print, Sep. 9,2008, pp. 1-30, available at K-theory archive, http : //www.math.uiuc.edu/K −

theory, no. 908.

41. J.-L. Colliot-Thelene, R. Parimala, V. Suresh, Patching and local-global princi-ples for homogeneous spaces over functions fields of p-adic curves, available athttp : //www.arxiv.org, no. 0812.3099v3, [math.AG], pp. 1-17, 16 Dec., 2009;or http : //math.uni − bielefeld.de/LAG/man/341.pdf , Dec. 2009, pp. 1-17.

42. E. Frenkel, X. Zhu, Global representation of double loop groups, E-print, http ://www.arXiv.org, no. 0810.1487v3 [math.RT], pp. 1-60, 17 Nov. 2008.

43. Ch. D., Gonzales-Aviles, Neron class groups and Tate- Shafarevich groups ofabelian varieties, http : //www.math.leidenuniv.nl/ ∼ asolk/monday/notes/gonzales − neron.pdf .

44. Ch. D. Gonzales-Aviles, Neron-Raunaud class groups of tori and the capit-ulation problem, J. Reine Appl. Math.,i(2010), E-print, pp. 1- 33, see alsohttp : //www.arXiv.org, no. 0903.3221v1, [math.NT], 18 March 2009.

45. I. Panin, A. Stavrova, N. Vavilov, On Grothendieck-Serre conjecture concerningprinciple G-bundles over reductive group schemes: I, E-print, pp. 1-27, avail-able at arXiv : 0905.1418v1, [math.AG], May 9, 2009, or http : //math.uni −bielefeld.de/LAG/man/35???.dvi.

46. I. Panin, On the Grothendieck-Serre conjecture concerning principle G-bundlesover reduc-tive group schemes:II, http : //math.uni − bielefeld.de/LAG/man/335.pdf , 8May, 2009, pp. 1-33.

46. I. Panin, Purity conjecture for reductive groups, Vestnik St. Petersburg U., vol.43(2010), no. 1, pp. 44-48.

47. J. Ayoub, S. Zucker, Relative Artin motives and reductive Borel-Serre com-pactifications of locally symmetric varieties, 3 March, 2011, pp. 1-111, avail-

12

able at arXiv:1002.2771v3, [math.AG]; see also. K-theory archive http ://www.uiuc.edu/K − theory, no. 933, 9 June, 2009, pp. 1-116;

48. C. Demarche, Methodes cohomologieques pour l’etude des points rationnels surles espaces homogenes, These, U. Paris-Sud XI, Orsay, France, pp. 1-211, Oct.2009, http : //www.math.u − psud.fr/ ∼ demarsche.pdf

49. C. Gonzales-Aviles, On Neron class groups of semiabelian varieties, E-print, pp.1-37, arXiv:0909.4803v1, [math.NT], 25 sept. 2009.

50. M. Wendt, A1-homotopy of Chevalley groups, Journ. of K-theory, v?? (2010),pp. 1-43.

51. M. Wendt, On rational A1-homotopy of Chevalley groups over global fields, http ://home.mathematik.uni − freiburg.de/arithmetische../wendt − rational.pdf

52. V. Chernousov, Variations on a theme of groups spliting over quadratic extension,E-print, Algebraic groups archive, Univ. Bielefeld, no. 354, pp. 1-21, 2009,http : //www.mathematik.uni − bielefeld.de/LAG/man/354.ps.gz.

53. G. Banaszak, W. Gaida and P. Krason, On the image of Galois ℓ-adic representa-tion for abelian varieties of type III, Tohoku Math. J., v. 62(2010), pp. 163-189;http : //webdoc.sub.dwdg.de/ebook/serien/e/mpi mathematik/2006/157/pdf ,pp. 1-24.

54. S. Gille, The first Suslin homology sheaf of a split simple connected algebraicsemisimple group, Jour. of algebra (2011),

55. Cortinas G., Haesemeyer C., Walker M., Weibel C., Toric varieties, monoidschemes and cdh-descent, K-theory archive, http : //www.math.uiuc.edu/K −

theory, no. 1002, May 20, 2011, pp. 1-45; or arXiv:1106.1889, [math.KT], June8, 2011.

56. A, Asok, Remarks on smooth A1-homotopy groups of smooth toric models, Math.Res. Lett., 18(2011), no. 2, pp. 353-356.

57. Yi Zhu, Homogeneous fibra-tions over curves, E-print, pp, 1-??, arXive:1111.2963v2, [math.AG], 20 May,2012.

58. C. Demarche, Le default d’approximation forte les groupes lineares connexes,Proc. London Math. Soc., 102(2011), no. 3, 563-597; see also arXiv:0906:3456v1,[math.NT], 18 June, 2009, pp. 1-33.

59. B. Kahn, Algebraic tori as Nisnevich sheaves with transfers, E-print,pp. 1-16, arXiv:1107.4938v1, [math.AG], 25 July, 2011; www.math.uni −

bielefeld.de/LAG/man/432.pdf .

60. D. Harbater, J. Hartmann and D. Krashen, Local-global principles for torsorsover arithmetic curves, E-print, arXiv:1108.3323v1, [math.AG], pp. 1-45, Aug16, 2011.

13

61. Ph. Gille, A. Pianzola, Torsors, reductive group schemes and affine Liealgebras, E-print, pp. 1-125, arXiv:1109v1, [math.RA], 15 sept. 2011;http://www.math.uni-bielefeld.de/ LAG/man/444.dvi.

62. S. Habibi, M. E. A. Rad, Motives of G-bundles, E-print, pp. 1-15, Dec. 18, 2011,arXiv:1112:411v1, [math.AG].

63. E. Frenkel, Langlands program, trace formulas, and their geometrization, arXiv :1202.211v1, [math.RT], 9 Feb. 2012, pp. 1-65.

64. K. Voelkel, M. Wendt, On A1-fundamental groups of isotropic reductive groups,arXiv:1207.2364, [math.AG], July 10, 2012.

65. B. Kahn, Ngan Thi Kim Nguyen, Modules de cycles et classes non ramifiees surun espace classifant, ArXiv:1211.0304v1, [math.AG], Nov. 1, 2012, pp. 1-????;or http : //www.math.uni − bielefeld.de/LAG/man/482.dvi

66. I. Panin. V. Petrov, Rationally isotropic exceptional projective homogeneousvarieties are locally isotropic, arxiv:1210.6695v1, [math.AG], 24 Oct. 2012, pp.1-???

67. R. Fedorov, I. Panin, A proof of Grothendieck-Serre conjecture on principle bun-dles over regular local rings containing infinite fields, e-print, arXiv:1211.2678v2,[math.AG], 25 April, 2012, pp. 1-20.

68. R. Fedorov, Affine grassmanians of group schmemes and exotic bundles overaffine lines, arXiv:1308.3078, [math.AG], pp. 1-19, Aug. 2013.

69. V. Chernousov, A. Merkuriev, Essential p-dimension of split simple grouos oftype An, Math. Annalen, 357(2013), no. 1, pp. 1-10.

70. K. Hutchinson, M. Wendt, On the third homology of SL2 and weak homotopyinvariance, E-print, arXiv:3069v1, [math.AG], 11 July, 2013, pp. 1-25.

71. R. Bitan, R. Koehl, A building theoretical approach to relative Tamagawanumber for quasi-split semisimple groups over global function fields, E-print,arXiv:1309.7641v1, [math.AG], [math.NT], pp. 1-25, 1 Oct. 2013.

3. APPLICATION TO THE HIGHER DIMENSIONAL

CLASS FIELD THEORY.

1. K. Kato, S. Saito, Global Class Field Theory of arithmetic Schemes, in: AlgebraicK-theory, Connections with Geometry and Topology?, Contemp. Mathematics,v. 55 (1986), pp. 255-332.

2. K. Kato, Conjectures on Etale and Nisnevich Cohomology and L-functions ofopen and singular arithmetic schemes, Letters to Ye. A. Nisnevich of March 11and 12, 1987.

14

3. K. Kato, A generalization of the Class Field Theory, Sugaky, 40 (1988), pp.289-311; Engl. transl. in ”Selected papers on Number Theory and AlgebraicGeometry” (Translated from Sugaku), AMS Translations, ser. 2, v. 172, (1996),pp. 31-59.

4. Y. Ihara, T. Saito, Introduction to the work of Kazuya Kato, Sugaku, 40 (1988),no. 4, pp. 339-344.

5. K. Kato, S. Saito, Notices on a Global Class Field Theory of arithmetic schemes,unpublished manuscript, 1989.

6. S. Saito, Arithmetic Theory of Arithmetic Surfaces, Ann. of Math., 129 (1989),547-589.

7. S. Saito, Some observations on Motivic cohomology of arithmetic schemes, Invent.Math., 89(1989), pp. 371-404; see also http : //www.springerlink.com/index/P082X0313882V 061.pdf

8. K. Kato, Generalized Class Field Theory, in ICM 1990, see item I-3 above.

9. W. Raskind, Abelian Class Field Theory of arithmetic schemes, see item I-5above.

10. M. Morishita, On the S-class number relations for algebraic tori..., see item II-2.10 above.

11. T. Szamuely, Sur la theorie des corps de classes pour les varietes sur les corpsp-adiques, Thesis, Orsay, 1998; see also http : //www.renyi.hu/ ∼ szamuely,pp. 1-32.

12. T. Szamuely, Sur la theorie des corps de classes pour les varieties sur les corpsp-adiques, Journ. fur die reine and Angw. math., b. 525 (2000), pp. 183-212;see also http : //www.atypon − link.com/WDG/doi/pdf/10.1515/crll.2000.66

13. A. Schmidt, M. Spiess, Singular Cohomology and Class Field theory of varietiesover finite fields, J. Reine Angew. Math., b. 527 (2000), pp. 13-36, http ://www.atypon− link.com/WDG/doi/pdf/10.1515/crll.2000.079; see also http ://www.math.uiuc.edu/K − theory, no. 362, 1999, pp. 1-25.

14. A. Schmidt, Absolute singular homology of arithmetic schemes, Preprint, 2000.

15. A. Schmidt, Class Field Theory (a topological point of view), see item I-37 above.

16. T. Yamasaki, Torsion zero cycles on a product of canonical lifts of elliptic curves,K-theory, v.31(2004), no. 4, pp. 289-306.

17. K. Sato, ℓ-adic class field theory for regular local rings, Math. Ann., v. 344(2009), no. 2, pp. 341-352; see also arXiv : 0709.3628v1, [math.NT], pp. 1-9.

18. M. Kerz, Higher class field theory and the connected component, E-print,pp. 1-23, available at http : //www.arXiv.org, no. 0711.4485v2, [math.AG],[math.NT], 25 Sep., 2008.

15

19. M. Kerz, Ideles in Higher dimension, Math. Res. Letters, v. 18 (2011), no. 4,pp. 699-713; see also arXiv:0907.5337v1, [math.NT], pp. 1-15, July, 2009.

20. T. Yamazaki, Brauer-Manin pairing, class field theory and motivic homology,E-print, pp. 1-30, arXiv:1009.4026v3, [math.NT], 1 June 2011.

21. J. Scholbach, Special L-values of motives, Diss., Univ. Freiburg, 158pp., Oct.2009, http : //www.freidocs.uni − freiburg.de/volltexte/7166/L − values.pdf .

22. J. Ayoub, Une version relative de la conjecture des periodes de Kontsevich-Zagier,E-print, pp. 1-54?, in K-theory archive, http : //www.math.uiuc.edu/K −

theory, Sept. 4, 2011.

23. Kahn, T. Yamazaki, Voevodsky motives and Weil reciprocity, E-print,arXiv:1108.2764v2, [math.AG], [math.NT], 29 Nov. 2012, pp. 1-40; orhal.archives − ouverts.fr/docs/00/75//88/85/Somekawa − V oevodsky23.tex,29 Nov. 2011.

24. M. Kerz, S. Saito, Chow group of 0-cycles with modulus and highdimensionalclass field theory, E-print, arXiv1304.4400v1, [math.AG], [math.NT], 16 April,2013, pp. 1-16pp??, 46Kb.

25. D. Osipov, Xinwen Zhu, Two-dimensional Contou-Carree symbol and reciprocitylaws, E-print, arXiv:1305.6032v1, [math.AG], May 26, 2013, pp. 1-52, 51Kb.

26. T. Geisser, A. Schmidt, Tame class field theory for singular varieties over alge-braically closed fields, E-print, arXiv:1309.4068v1, [math.AG], 16 Sep. 2013,pp. 1-32.

4. APPLICATIONS TO THE ALGEBRAIC K-THEORY.

1. Ye. Nisnevich, 1989, see item II-1.3. above.

2. Ye. Nisnevich, Some new cohomological description of the Chow group of alge-braic cycles and the coniveau filtration, Preprint, 1991, pp. 1-138.

3. R. W. Thomason, Th. Trobauch, Le theoreme de localisation en K-theoriealgebrique, Comptes Rendus Acad. Sciences, Paris, t. 307 (1988), pp. 829-831.

4. R. W. Thomason, Th. Trobauch, Higher algebraic K-theory of schemes andderived categories, in: ”The Grothendieck Festschrift”, v. III, Progress in Math-ematics, v. 88, Birkhauser, Boston- Basel, 1990, pp. 245-495.

5. R. W. Thomason, ICM 1990 in Kyoto, invited talk, see item I-4 above.

6. J.-L. Colliot-Thelene, R. Hoobler, B. Kahn, The Bloch-Ogus -Gabber Theorem,in: ”Algebraic K-theory, proc. 2nd Great Lake Conf. held at Toronto, 1996”,Fields Institute Communications, v. 16, V. Snaith (ed.), Amer. Math. Soc.,Providence, R. I., 1997, pp. 31-94.

16

7. S. A. Mitchel, Hypercohomology spectra and Thomason’s descent Theorem, in:”Algebraic K-theory, Proc. 2nd Great Lake Conf. held in Toronto”, 1996, FieldsInstitute Communications, v. 16, V. Snaith (ed.), Amer. Math. Soc., Providence,R. I., 1997, pp. 221-277,

8. B. Kahn, Quillen-Lichtenbaum Conjecture at the prime 2, K-theory, v. 25 (2002),no. 1, pp. 99-138.

9. D. Arlettaz, C. Banaszak, W. Gajda, On Product in algebraic K-theory, Comm.Math. Helv., v. 74 (1999), pp. 476-506.

10. J. Rognes, C. Weibel, M. Kolster, Two primary algebraic K- theory of rings ofintergers, J. Amer. Math. Soc., 13 (2000), No. 1. pp. 1-54, see also http ://www.math.uiuc.edu/K − theory, no. 220.

11. Ch. Weibel, The negative K-theory of singular surfaces, Duke M. J., v. 108(2001), no. 1, pp. 1-35; see aslo http : //math.uiuc.edu/K − theory, no. 367,1998, pp. 1-27.

12. E. Friedlander, M. E. Walker, Semi-topological K-theory of real varieties, in ”Al-gebra, Arithmetic, and Geometry”, Proc. Internat. Colloq. Mumbai, 2000), partI, Bombey, 2002, pp. 219-326, see also http : //www.math.uiuc.edu/K− theory,no. 453, 2000, pp. 1-85, or http://www.math.unl.edu/ mwalker5/papers/KRsemi.pdf.

13. B. Kahn, Cohomologie non ramifiee des quadriques, in Izboldin O., KarpenkoN., vishik A., ”Geometric methods in the theory of quadratic forms, Lenz,2001”, Lect. Notes in Math., 1835 (2004), pp. 1-23; see also http ://www.math.uiuc.edu/K − theory, no. 478, 2001, pp. 1-23.

14. T. Geisser, L. Hesselholt, K-theory and topological cyclic homology of smoothschemes over discrete valuation rings, Transact. AMS, v. 358(2004), no. 1, pp.131-145; see also http : //www.math.uiuc.edu/K − theory, no. 477.

15. M. Karoubi , Ch. Weibel, Algebraic and Real K-theory of real varieties, Topol-ogy, 42 (2003), no. 4, pp. 715-742; see also http : //www.math.uiuc.edu/K −

theory, no. 473, 2001, pp. 1-37

16. R. Cohen, P. Lima-Filho, Holomorphic K-theory, algebraic cocycles and loopgroups, in K-theory, v. 23, no. 4, pp. 345- 376; see also http ://www.math.tamu.edu/ ∼ plfilho/research/papers/holok.ps

17. B. Kahn, K-theory of semi-local rings with finite coefficients and etale co-homology, K-theory, v. 25 (2002), no.2, pp. 99-138; see also http ://www.math.uiuc.edu/K − theory, no. 537, 2002, pp. 1-46.

18. E. Friedlander, M. Walker, Rational isomorphisms between K- theories and co-homology theories, Invent. Math., v. 154 (2003), pp. 1-61, see also http ://www.math.uiuc.edu/K − theory, no. 557, 2002.

19. P. Balmer, Witt cohomology, Mayer-Vietoris, Homotopy invariance and the

17

Gersten conjecture, pp. 1-20, 2002, http : //www.math.ethz.ch/ ∼

balmer/Cohom.pdf

20. J. Hornbostel, Sur la K-theorie des categories hermitiennes, These, 2001, http ://www.math.jussieu.fr/ ∼ Karoubi/These/Hornbostel.pdf

21. J. Hornbostel, A1-representability of hermitian K- theory and Witt groups,Topology, v. 44, no. 3 (2005), pp. 661- 687, see also http ://www.math.uiuc.edu/K − theory, no. 578.

22. J. Hornbostel, Balmer Witt groups, Karoubi tower and A1 -homotopy, Preprint,2002, 13pp., available in http : //www.nwu.edu/faculty

23. V. Voevodsky, A possible approach to the motivic spectral sequence for algebraicK-theory, Recent progress in the homotopy theory (Proc. Conf. at Johns Hop-kins Univ., Baltimore, MD, 2000), pp. 371-379, Contemporary. Math., v. 293,AMS, RI, 2002, see also: http : //www.math.uiuc.edu/K − theory, no. 469,2001. pp. 1-11.

24. M. Walker, Thomason’s theorem for varieties over algebraically closed fields,Trans. AMS, v. 256 (2004?), pp. 2569-2648 (pp. 2596, 2607-2608).

24. E. Friedlander, Haesemeyer Ch., M. Walker, Techniques, computations and con-jectures for semi-topological K-theory, Math. Ann., b. 330 (2004), no. 4, pp.759-807. see also the K-theory archive, http : //www.math.uiuc.edu/K−theory,no. 621 (2003), pp 1-44.

25. P. Balmer, Witt groups, in: ”Handbook of Algebraic K-theory”, Springer, 2005,pp. 539-576, see also http : //www.math.etzh.ch/ ∼ balmer/Pubfile/W −

handbook.pdf , pp. 1-35.

26. P. Balmer, Introduction to triangular Witt groups and survey of applications,in: ”Algebraic and Arithmtic theory of quadratic forms”, Proceedings of theInternational Conference held at the Univ. of Talca, 2002, eds. R. Baeza, J.Hsia, W. Jacobs, A. Prestel, Contemp. Math. 344 (2004), pp. 31-58, AMS, RI;see also http : //www.math.ethz.ch/ ∼ balmer/Pubfile/survey.pdf .

27. C. Haesemeyer, Descent properties for homotopy K-theory, Duke Math. J., v.125 (2004), no. 3, 585-615; see also www.math.ucla.edu/ ∼ chh/descent.pdf ; anearlier version: http : //www.math.uiuc.edu/K − theory, no. 650, pp. 1-21.

28. I. Panin, Homotopy invariance of the sheaf WNis and its cohomology, in”Quadratic forms, linear algebraic groups and cohomology, eds. J.C. Colliot-Thelene, S. Garibaldi, R. Sajatha, V. Suresh, Development of math., v. 18,Springer, 2010, pp. 325-335; see also http : //www.math.uiuc.edu/K − theory,No. 715, Nov. 2004, pp. 1-10.

29. Cortinas, C. Haesemeyer, M. Schlichting, C. Weibel, Cyclic homology, cdh-cohomology and negative K-theory, Annals of Math., 165 (2007), pp. 1-25, see also http : //annals.math.princeton.edu/issues/2007/F inalF iles/

18

CortinasHaesemeyerSchlichtingWeibel/F inal.pdf or http : //www.math.uiuc.edu/K − theory, no. 722.

30. A. Rosenschon, P.-A. Ostvaer, Homotopy limit problem for two-primary algebraicK-theory, Topology, v. 44 (2005), no. 6, pp. 1159-1179.

31. A. Nenashev, Gysin maps in Balmer-Witt theory, Preprint, 2005, pp. 1-22,available at the K-theory archive, http : //www.math.uiuc.edu/K − theory, no.760.

32. S. Mochizuki, Motivic interpretation of Milnor K-groups attached to Jacobiansvarieties, Preprint, March 2006, pp. 1-29, available at the K-theory archivehttp : //www.math.uiuc.edu/K − theory, no. 774.

33. G. Cortinas, C. Haesemeyer, C. A. Weibel, K-regularity, cdh- fibrant Hochschildhomology, and a conjecture of Vorst, Journ. AMS, May, 2007, pp. 1-15, electroniced.: http : //www.ams.org/jams, see also http : //www.math.uiuc.edu/K −

theory, no. 783.

34. A. Rosenschon, P.-A. Ostvaer, Descent for K-theories, Journ. of Pure and Appl.Algebra, v. 206 (2006), n. 1-2, pp. 141-152.

35. J. Riou, Operations sur la K-theorie algebrique et regulateurs via la theoriehomotopique des schemas, Comp. Rend. Acad. Sci. Paris, (2006), pp. ??.

36. J. Riou, Operations on K-theorie algebrique et regulateurs via theorie homo-topique des schemes, These, Univ. Paris VII, July 2006, pp. 1-216, available atthe K-theory archive http : //www.math.uiuc.edu/K − theory, no. 793, 2006;or hal.inria.fr/docs/00/13/39/PDF/these − riou.pdf , 28 Feb. 2007.

37. C. Mazza, Voevodsky’s motives and K-theory, Lectures at the Sedano WinterSchool on K-theory, Jan. 2007, pp. 1-64, http : //cms.dm.uba.ar/Members/gcorti/workinggroup.swisk/en/sem.pdf .

38. M. Schlichting, Higher K-theory according to Quillen, Thomason and oth-ers, in Topics in Algebraic and topological K-theory (Lectures at the SedanoWinter School on K-theory, Jan. 2007), eds. Baum P. F., Cortinas G.,Meyer R., pp.??, Lect. Notes in Math. v. (2010); see also http ://cms.dm.uba.ar/Members/gcorti/workinggroup.swisk/en/sem.pdf .

39. T. Geisser, Parshin’s conjecture revisited, in: K-theory and noncommutativegeometry, eds: G. Cortinas, J. Cuntz, M. Karoubi, R. Nest, C. Weibel, EMSseries on congress reports, EMS Publishing House, Zurich, 2008, pp. 413-426;see also http : //www.arXiv.org : math.KT/0701630, pp. 1-14.

40. D. Eriksson, Analytic torsion and Deligne-Riemann-Roch, Preprint, 2006, pp.1-21, available at http : //www.dma.ens.fr/ eriksson/Analytictorsion1.ps,

41. C. Weibel, Trieste lectures on the Bloch-Kato conjecture, Preprint, pp. 1-28,2007, available at http : //www.math.rutgers.edu/ ∼ weibel.

19

42. B. Kahn, M. Levine, Motive of Severi-Brauer varieties and K-theory of sim-ple algebras Abel Symposium, Oslo, 2007, pp. 1-57, available at http ://folk.uio.no/abelsymposium/levine/AzumayaBeamer4.pdf

43. B. Kahn, M. Levine, Motives of Azumaya algebras, E-print, to ap-pear in J. Institute de Mathematique de Jussieu (2010), see also http ://www.math.uiuc.edu/K − theory, no. 875, Nov. 3, 2009 (the last revision).

44. B. Kahn, Homotopical approaches to SK1 and SK2 of central sim-ple algebras (joint work with Mark Levine), talk at the Confer-ence on quadratic forms, Utalca, Chile, 2007, available at http ://people.math.jussieu.fr/ ∼ kahn/preprints/SK1 − LLANquihue.pdf orinst − mat.utalca.cl/qfc2007/Talks/kahn.pdf

45. M. Spies, T. Yamasaki, A counterexample to generalizations of the Milnor-Block-Kato conjecture, Preprint, pp. 1-13, 2007, available at http ://www.math.uiuc.edu/K − theory, no. 862.

46. I.Panin, K. Pimenov, O. Roendigs, On the relation of Voevodsky’s al-gebraic cobordism to Quillen’s K-theory, E-print, 2007, pp. 1-18,available at arXiv:0709.4124v1 [math.AG]; an older version at http ://www.math.uiuc.edu/K − theory, no. 847.

47. G. Cortinas, C. Haesemeyer, M. Walker, C. Weibel, The K-theory of toric vari-eties, E-print, 2007, pp. 1-17, available at arXiv : 0709.2087v1 [math.KT ].

48. A. Asok, Equivariant vector bundles on certain affine G-varieties, Pure andAppl. Mathematics Quaterly, v. 2, no. 4, pp. 1085-1102, see also arXiv :math/0604344v1, [math.AG].

49. A. Asok, B. Doran, Vector bundles on contractible smooth schemes, Duke Math.Jour., v. 143 (2008), no. 3, 513-530; also arXiv : 0710.3607v, [math.AG], Nob.2007, pp, 1-15.

50. D. Gepner, V. Snaith, On the motivic spectra representing algebraic cobor-dism and algebraic K-theory, Docum. Math., 14(2009), pp. 359-396 -http : //math.uni− bielefeld.de/documenta/vol− 14/14, dvi; an earlier version:arXiv:07122817v1, [math.AG], pp. 1-20, 17 Dec. 2007.

51. G. Cortinas, C. Haesemeyer, M. Walker, C. Weibel, Bass’ NK groups andcdh-fibrant Hochschild homology, Preprint, available at the Algebraic K-theoryarchive, http : //www.math.uiuc.edu/K − theory, no. 883, pp. 1-30; see alsoarXiv : 0802.1928, no. [math.KT].

52. M. Spitzweck, P.-A. Ostvaer, The Bott inverted infinite projective space in homo-topy algebraic K-theory, Bull. London Math. Soc., 41(2009), no. 2, pp. 281-292;see also preprint http : //www.math.uio.no/paularne/bott.pdf

53. M. Schlichting, The Mayer-Vietoris principle for Grothendieck- Witt groups ofschemes, E-print, pp. 1-66, 28 Nov. 2008, available at arXiv : 0811.4632v1,

20

[math.AG], see also http : //www.math.lsu.edu/ ∼ mschlich/research.html.

54. N. Naumann, M. Spitzweck, P.-A. Ostvaer, Chern classes, K-theory and Landwe-ber exactness over non-regular base schemes, in: Motives and algebraic cycles: acelebration in honour of Spencer J. Bloch, Fields Institute communications, v. 56(2009), pp. 307-322; see also http : //www.arxiv.org, no. 0809.0267, [math.AG],Sept. 2008, pp. 1-14.

55. J. Fasel, Some remarks on orbits sets of unimodalar rows, E-print, Aug. 2008,pp. 1- 18, available from the K-theory archive, http : //www.math.uiuc.edu/K−

theory, no. 905.

56. J. F. Jardine, K-theory presheaf of spectra, New topological con-texts for Galois theory and algebraic geometry, BIRS, 2008, Geome-try - Topology Monographs, v. 16 (2009), pp. 151-176, availableat http : //mps.warwick.ac.uk/gtm/2009/16/p007.xhtml, see also http ://www.math.uiuc.edu/K − theory, no. 908, Sept. 2008, pp. 1-22.

57. A. Krishna, On the negative K-theory of schemes in finite characteristic, Journ.of Algebra, 322 (2009), pp. 2118-2130; see also E-print, 3 Nov., 2008, pp. 1-13,http : //www.arXiv.org, no. 0811.0302v2, [math.AG].

58. T. Geiser, L. Hesselholt, On the vanishing of negative K-groups, Math. Annalen,v.347 (2010), no. 2?, pp. ??; see also arXiv:0811.0652v1, [math.AG], Nov. 2009,pp. 1-11.

59. L. Rubio I Pons, Fibrant presheaves of spectra and Guillen- Navarro extension,pp. 1-9, http : //rendiconti.math.unipd.it/forthcoming/rubiof ibrantlogo.pdf ,see also http : //www.upcommons.ups.edu/e − prints/bitstrim/2117/2354/1/rubio − fdfabs.pdf .

60. L. Rubio I. Pons, Categories de descens. Tesis, Barcelona, 2008, pp. 1-159;http : //tesisenxarxa.net/TESIS V PC/AV AILABLE...

61. M. Levine. C. Serpe, On a spectral sequence for equivariant K-theory, K-theory, 38(2008), no. 2, pp. 177-222, http : //springerlink.com/content/pj11n22133262k9l/fulltext.pdf ; http : //www.math.neu.edu/ ∼ Levine/EquivSpecSeq.pdf .

62. A. Nenashev, On the Witt groups of projective bundles and splitquadrics: geometric reasoning, Jour. of K-theory, 2008, http ://journals.cambridge.org/production/action/cjoGetFulltext?fulltextid =1956088.

63. D. Orlov, Formal completions and idempotent completions of triangulated cate-gories of singularities, Advances in Mathematics, 226(2011), no.1, pp. 206-217;see also http : //www.arXiv.org, no. 0901.1859v1, [math.AG], Jan. 2009, pp.1-12.

64. D. Eriksson, A Deligne-Riemann-Roch isomorphism I: Preliminaries on virtual

21

categories, available at arXiv : 0904.4059v1, [math.AG], pp. 1-71, 26 April,2009.

65. N. Yagita, Note on Witt group and K0-theory of complex Grassmannians, E-print, Linear algebraic groups archive, Univ. Bielefeld, 2009, no. 325, pp. 1-10,http : //www.math.uni − bielefeld.de/LAG/man/325.ps.

66. A. Nenashev, Projective push forwards in the Witt theory of algebraic varieties,Advances in math., v. 220(2009), no. 6, pp. 1923-1944; see also Preprint, pp.1-??, 2008; http : //www.math.uiuc.edu/K − theory, no. 848

67. G. Cortinas, Ch. Haesemeyer, M. Walker, C. Weibel, K-theory of cones of smoothvarieties, E-print, available at arXiv : 0905.4642v2, [math.KT]. 28 May. 2009,pp. 1-17; or K- theory archive: http : //www.math.uiuc.edu/K − theory, no.???.

68. M. Wendt, Stabilization in algebraic K-theory and group homology,Preprint, Dec. 2009, pp. 1-21, http : //home.mathematik.uni −

freiburg.de/arithmetishce − geometrie/preprints/wendt − stabilization.pdf .

69. J. Riou, Algebraic K-theory, A1-homotopy and Riemann- Roch theorems, J.of Topology, v. 3, no. 2 (2010), pp. 229-264; see also arXiv:0907.2338v1[math.AG], pp. 1-39, July 2009, or http : //www.math.uiuc.edu/K − theory.

70. O. Rondigs, M. Spitzweck, P. Ostvaer, Motivic strict ring model for K-theory,Proc. AMS, 138(2010), 3509-3520; see also arXive:0907.4121v1, [math.AT], 23July, 2009, or http : //www.archive.uisc.edu/K−theory, no. 937, July 23, 2009.

71. M. Spiess, T. Yamazaki, A counterexample to generalization of the Milnor-Bloch-Kato conjecture, J. K-theory, 4(2009), no. 1, 77-90.

72. Weibel C., The norm residue isomorphism theorem, Journ. of Topology, v. 2(2009), 346-372; see also http : //www.math.uiuc.edu/K − theory, no. 934,June, 2009,

73. B. Kahn, Cohomological approaches to SK1 and SK2 of central simple alge-bras, Documenta Math., Extra volume: Andrei A. Suslin sixtieth birthday,2010, pp. 317-369, http : //www.math.uni − bielefeld.de/documenta/vol −suslin/kahn.dvi; see also E-print, Nov. 2009, pp. 1-54, available at the Linearalgebraic groups archive, Bielefeld, No. 368: http : //www.mathematik.uni −bielefeld.de/LAG/man/368.ps.gz,

74. Ch. Serpe, Descent properties of equivariant K-theory, 12 Feb. 2010, pp. 1-13,available at arXive:1002.2565v1, [math.KT].

75. D. Isaksen, A. Shkembi, Motivic connective K-theories and the cohomology ofA(1), E-print, 11 Feb. 2010, pp. 1-30, available at ArXiv:1002:2368v1.

76. D.-Ch. Cisinski, Descente propre en K-theorie invariante par homotopie, E-print,pp. 1-30, 7 March, 2010, arXiv:1003.1487v1, [math.AG].

22

77. G. Cortinas, C. Haesemeyer, M. Walker, A negative answer to a question of Bass,Proc. AMS, 139(2011), pp. 1187-1200; http : //arXiv.org/abs/1004.3829v1, pp.1-13?, 22 April, 2010,

78. A. Krishna, P.-A. Ostvaer, Nisnevich descent for Deligne-Mumford stack, Ad-vances in math., v. 231, no. 6 E-print, pp. 1-34, 10 May, 2010, arXiv:1005.0968.

79. B. Kahn, Relatively unramified elements in cycle modules, Preprint, March, 2010,pp. 1-18, http : //www.math.jussie.fr/ ∼ kahn/preprints/modcyclnr.pdf

80. A. Berrick, M. Karoubi, P. A. Ostvaer, Periodicity of Hermitian K-groups,Jour. of K-theory, pp. 1-62, 2011; see also arXiv:1101.2056v1, [math.KT] orwww.math.uiuc.edu/K-theory, no. 990, 10 Jan. 2011.

81. Y. Kim, Motivic symmetric spectrum ring representing algebraic K-theory, Dissertation, April. 2010, pp. 1-91, Univ. Illinois, Ur-bana, http : //www.math.uiuc.edu/ ∼ ykim33/thesis.pdf , or http ://udini.proquest.com/view/motivic− symmetric− ring − spectrum− ... 93pp.

82. J. Heller, M. Voineagu, Equivariant semi-topological invariants, Atiyah KR-theory, and real algebaraic cycles, E-print, Oct. 2010, pp. 1-39, arXiv:1008.3685,[math.AG].

83. M. Spitzweck, P. A. Ostvaer, Motivic twisted K-thery, E-print, Aug. 2010,pp. 1-35, K-theory archive, http : //www.uiuc.edu/K − theory, no. 969; orarXiv:1008.4915, [math.AT].

84. M. Zibrowius, Witt groups of complex cellular varieties, Documenta Math., v.16 (2011), pp. 465-510; see also arXiv:1011.3757v3, [math.KT], 27 June, 2011,pp. 1-45??

85. E. S. Tripathi, Orthogonal Grassmannians and Hermitian K-theory in A1-homotopy theory of schemes, Dissertation, Louisianna State Univ., 2010, pp.1-135. etd.lsu.edu/docs/available/etd − 11152010 − 145059/.../tripathidiss.pdf

86. M. Schlichting, The homotopy limit problem and (etale) Hermitian K-theory,E-print, 23 Nov. 2010, pp. 1-6, arXiv:1011.4977v1, [math.KT].

87. A. J. Berrick, M. Karoubi, M. Schlichting, P. A. Ostvaer, The homotopy fixedpoint theorem and the Quillen-Lichtenbaum conjecture in hermitian K-theory,E-print, pp. 1-16, arXive:1011.4977v2, [math.KT], Aug. 25, 2011; also K-theoryarchive, http : //www.math.uiuc.edu/K − theory, no. 1009, pp. 1-16.

88. B. Kahn, T. Yamazaki, Somekawa’s K-groups and Voevodsky’s Hom groups,E-print, K-theory archive, http://www.math.uiuc.edu/ K-theory, no. 1005, pp.1-33, Aug. 12, 2011; arXiv:080:2764, pp. 1-33, Aug. 15, 2011.

89. P. Pascual, L. Rubio Pons, Algebraic K-theory and cubical descente, Homologytheory, homotopy theory and appl., v. 11 (2009), no. 2, pp. 5-25.

90. Pere Pascual, On cdh-descent (after Haesemyer at all), http//www.ma1.upc.edu/

23

recerca/preprint/preprints − 2011/F itxers/prepr201101.pascual, 2011, pp. 1-15??.

91. A. Knizel, A. Neshitov, Algebraic analogue of Atiyah’s theorem, E-print, K-theory archive, http : //www.math.uiuc.edu/K − theory, no. 1016, Nov. 20,2011, pp. 1-18.

92. S. Kelly, Vanishing of negative K-theory in positive characteristic, E-print, pp.1-15, Dec. 23, 2011, arXiv:1112: 5206v1, [math.AG].

93. A. Krishna, Completion theorem for equivariant K-theory, E-print, pp. 1-38,arXiv:1201.5766v1, [math.AG], 27 Jan. 2012.

94. M. Zibrovius, Witt groups of complex varieties, Thesis, U. Cambridge,April 2011, pp. 1-119; or http : //www2.math.uni − wuppertal.de/ ∼

zibrowiu/Research/Zibrowius Thesis.pdf , or http : //www.dspace.cam.ac.uk/bitstream/1810/239413/1/Zibrowius Thesis.pdf .

95. M. Zibrowius, Comparing Grothendieck-Witt groups of complex varieties andits real forms, Preprint, pp. 1-37, 2011, www.dspace.cam.ac.uk/bitstream/1810/236624/GWFinal.pdf , or http : //www2.math.univ − wupertal.de/ ∼

zibrowius.pdf .

96. C. Barwick, On the algebraic K-theory of higher categories, I. The universalproperty of Waldhausen K-theory, E-print, arXiv:1204.3607, [math.KT] April16, 2012, pp. 1-70.

97. A. Asok, Splitting of vector bundles and A1-fundamental groups of higher di-mensional varieties, arXiv:1103.1723v1, [math.AG], [math.KT], 9 Mar. 2011, pp.1-44.

98. A. Asok, J. Fasel, A cohomological classification of vector bundles on smoothaffine threefolds, E-print, arXiv:1204.0770v3, [math.AG], 31 May, 2012, pp. 1-49.

99. A. Asok, J. Fasel, Algebraic vector bundles on spheres, E-print, 1204.4538v2,[masth.AG], pp. 1-28, 31 May, 2012.

100. G. Garkusha, Algebraic Kasparov K-theory. II, E-print, arXiv:1206.0178v1,[math.KT], June 1, 2012, pp. 1-33.

101. M. Morrow, A singular analogue of Gersten conjecture and application of K-theoretic adeles, E-print, pp. 1- ???. arXiv:1208.0931, [math.KT], Aug, 3, 2012.

102. M. Schlichting, Hermitian K-theory, derived equivalences, and Karoubi’s fun-damental theorem, E-print, pp. 1-110, arXiv:1209.0848v1, [math.KT], Sep. 5,2012, 98Kb.

103. F. Ivorra, K. Rulling, K-groups of reciprocity functors, E-print, pp. 1-68,arXiv:1209.12.17v2, [math.KT], 12 Feb. 2013.

104. A. Asok, J. Fasel, Splitting vector bundles outside the stable range and homo-

24

topy theory of punctured affine spaces, E-print, pp. 1-41, arXiv:1209.5631v2,[math.AG], [math.KT], 5 Nov. 2012.

105. G. Garkusha, I. Panin, On the motivic spectral sequence, arXiv:1210.2242v1,[math.AG]. [math.KT], [math.AT], 8 Oct. 2012, pp. 1-???

106. M. Morrow, Pro H-unitality, pro cdh-descent for K-theory and applications tozero-cycles, E-print, arXiv:1211.1813v2, [math.KT], pp. 1-???, 21 July, 2013.

107. Doran B., Jun Yu., Algebraic vector bundles on punctures and smooth quadrics,14pp., arXiv:1303.0575v1, [math.GR], 3 Mar. 2013.

108. S. Mochizuki, Non-xonnective K-theory of relative exact categories, E-print,arXiv:1303.4133v1, Mar. 18, 2013, pp. 1-??.

109. M. Wendt, Units in Grothendieck-Witt rings and A1-spherical fibrations, E-print, arXiv:1304.5922v1, [math.AT], 22 April 2013, pp. 1-19, 55Kb.

110. J. Shih, On the negative K-theory of singular varieties,E-print, arXiv:1306.3688v1, [math.AG], [math.KT], June 16, 2013, pp. 1-24,or escholarshop.org.

111. H. Po, I. Kriz, K. Ormsby, The homotopy limit problem for hermitian K-theory,equivariant motivic homotopy and motivic real cobordism, Preprint, 2012?, 50pp.http : //www.math.mit.edu/ ∼ ormsby/ar1105.pdf

112. D. C. Cisinski, Descente par eclatement en K-theorie invariante par ho-motopie, Annals of Math., v. 177 (2013), pp. 425-448; http ://annals.math.princeton.edu/?p = 7216.

113. G. Carlsson, A geometric reformulation of the representational assembly con-jecture for the K-theory of fields with pro-ℓ absolute Galois group, E-print,arXiv:1309.5649v1, pp. 1-65???, 24 Sept. 2013.

114. G. Carlsson, R. Joshua, Galois descent for completed algebraic K-theory, E-print,arXiv:1309.6045v2, [math.KT], [math.AT], pp. 1-36, 26 Sept. 2013.

115. M. Schlichting, G. S. Tipathi, Geometric models for higher Grothendieck-Wittgroups in A1-homotopy theory, E-print, arXiv:1309.5818v1, [math.KT], pp. 1-20???, 23 Sep. 2013.

116. O. Podkopaev, The equivalence of Grayson and Friedlander - Suslinspectral sequences, Dissertation, May 2012, Northwestern Univ., E-print,arXiv:1309.5797v1, [maht.KT], pp. 1-45, 1 Oct. 2013.

5. APPLICATIONS TO A STUDY OF ALGEBRAIC

CYCLES, THEIR INTERSECTIONS AND THE

PICARD AND HIGHER CHOW GROUPS

1. Ye. Nisnevich, see item II-4.2 above.

25

2. A. A. Suslin, Algebraic K-theory and Motivic cohomology, ICM 1992 in Zurich,see item I-6 above.

3. C. Pedrini, C. Weibel, The divisibility of the Chow group of zero cycles on singularsurfaces, K-theorie, Les contributions du Colloque Internationelle, Strassbourg,Asterisque, t. 226 (1994), pp. 371- 409.

4. Ch. Weibel, Picard group is a contractible functor, Invent. Math., v. 103 (1991),351-377.

5. B. Kahn, A sheaf-theoretic reformulation of the Tate Conjecture, Preprint, 1997,pp. 1-53, in http : //www.math.uiuc.edu/K − theory, no. 247.

6. A. Suslin, V. Voevodsky, Relative Cycles and Chow sheaves, in: Voevod-sky, Suslin, Friedlander, ”Cycles, Transfers and Motivic Cohomology Theo-ries”, Ann. of Math. Studies, v. 143, 2000, pp. 10-86; see also http ://www.math.uiuc.edu/K − theory, No. 35, 1994.

7. E. M. Friedlander, V. Voevodsky, Bivariant cycles cohomology, in: V. Voevodsky,A. Suslin, E. Friedlander, ”Cycles, Transfers and Motivic Homology Theories”,Annals of Math. Studies, v. 143, 2000, Princeton Univ. Press. pp. 138-187; seealso http : //www.math.uiuc.edu/K − theory, no. 368, s?, 1999.

8. A. Vishik, Integral motives of quadrics, Preprint, MPI-1998-13, pp. 1-82, http : //www.mpim − bonn.mpg.de/preprints/send?bid = 286.ps.webdoc.sub.gwdg.de/ebook/serien/e/mpimathematik/1998/13.ps.

9. A. Vishik, On the dimension of anisotropic forms in In, Preprint, Max PlankInst., 2000, pp. 1-41.

10. A. Vishik, On torsion elements in the Chow-groups of quadrics, Preprint, MaxPlank Inst., 2000, pp. 1-10.

11. F. Deglise, Interpretation motivique de la formule d’exces d’intersection, ComptesRendus Acad. Sci, Paris, t. 332 (2002), no. 1, pp. 1-6.

12. F. Deglise, Quelques complements sur les modules de cycles, Preprint, Nov. 2003,pp. 1-30, available at the K-theory arXiv: http : //www.math.uiuc.edu/K −

theory, no. 669.

13. F. Deglise, Motivic interpretation of the excess intersection formula and ramifiedcase, Lect. at Institut Henri Poincare, Paris, Preprint, 2004, pp. 1-12, availableat http : //www.math.univ − paris13.fr/ ∼ deglise.

14. T. Yamazaki, Torsion zero-cycles on a product of canonical lifts of elliptic curves,K-theory, v. 31 (2004), pp. 289- 306.

15. R. Joshua, Higher intersection theory on algebraic stacks: II, K-theory, v. 27(2002), pp. 197-244.

16. N. Yagita, Chow groups of classifying spaces of extraspecial p-groups, in ”Recentprogress in the homotopy theory”, Proc. of the Conf. at JHU, Baltimore, MD,

26

2000), eds. M. Davis, J. Morava, W. S. Wilson, N. Yagita, Contemp. Math., v.293, AMS, RI, 2002, pp. 397-409.

17. Yagita N., The image of the cycle map of the classifying space of the exceptionalgroup F4, J. Math. Kyoto Univ., v. 44 (2004), pp. 181-191.

18. P. Guillot, Algebraic cycles, cobordisms and the cohomology of classifyingspaces, Thesis, Cambridge Univ., April 2005, pp. 1-86, available at http ://www.dpmms.cam.ac.uk/research/php.pdf , or http : //www − irma.u −

strasbg/guillot/research/phd/phd.pdf

19. B. Kahn, Algebraic K-theory, algebraic cycles and arithmetic geometry, in”Handbook of K-theory”, eds. E. Friedlander and D. Grayson, Springer, 2005,pp. 351-428; see also http : //www.math.jussieu.fr/ ∼ kahn, pp. 1-76.

20. B. Kahn, The full faithfulness conjectures in characteristic p, in:AuthordesMotifs, Ecole d’ete de l’IHES, 17-29 jullet 2006, pp. ???, available athttp : //www.math.jussieu.fr/ ∼ kahn/preprints/IHES0706.pdf

21. M. Rost, On the basic correspondence of splitting varieties, Preprint, Oct.-Nov. 2006. pp. 1-43; availabe at http : //www.math.uni − bielefeld.de/ ∼

rost/data/bkc − c.ps.gz.

22. F. Deglise, Transferts sur les groupes de Chow with coefficients, Math. Zeit.,256(2006), no. 2, pp. 315-343.

23. J. Horbostel, Oriented Chow groups, Hermitian K-theory and the Gersten Con-jecture, Manuscripta Math., b. 125 (2008), no. 3, pp. 275-284; see alsohttp : //www.math.uiuc.edu/K − theory, no. 835, pp. 1-14, April 17, 2007.

24. S. Gorchinsky, V. Guletskii, Motives and representability of algebraic cycles onthreefolds over a field, E-print, pp. 1-22, arXiv:0806.0173v1, [math.AG], 1 June,2008.

25. J. Heller, M. Voineagu, Vanishing theorems for real algebraic cycles,arXiv:0909.0769v1, [math.AG], 3 Sept. 2009, pp. 1-51.

26. G. Quick, Algebraic cycles and etale cobordism, E-print, pp. 1-22,arXiv:0911.0584v1 [math.AG], 4 Nov., 2009.

27. A. Krishna, A cdh-approach to zero-cycles on singular varieties, E-print, pp.1-47, 1 March 2010, arXiv:1003.0264v1, [math.AG].

28. S. Kondo, S. Yasuka, Product structures in motivic cohomology and higherChow groups, preprint, pp. 1-16, 2010, available at http : //db.ipmn.jp/sysimgipmu/367.pdf .

29. A. Asok, Ch. Haesemeyer, The 0-th stable A1-homotopy sheaf and quadraticzero cycles, E-print, pp. 1-45, arXiv:1108.3854v1, [math.AG], Aug. 20, 2011.

30. A. Asok, C. Hasemeyer, F. Morel, Rational points vs 0-cycles of deg. 1, in stableA1 homotopy, Preprint, http : //www.bcf.usc.edu

27

31. J. Heller, M. Voineagu, Remarks on filtrations of the homology groups of realvarieties, E-print, pp. 1-18, in arXiv:1110.1836v1, [math.AG], 9 Oct. 2011.

32. B. Kahn, The full faithfulness conjecture in characteristic p, E-print, pp. 1-61,arXiv:1209.4322v1, [math.AG], [math.NT], Sept. 19, 1209, 51Kb.

33. S. Bloch, H. Esnault, M. Kertz, p-adic deformations of algebraic cycle classes,E-print, arXiv:1203,2776, [math.AG], pp. 1-34, 13 March, 2012.

34. T. Hiranouchi, On certain product of algebraic groups over finite fields,arXiv:1209.4457v2, [alg.KT], pp. ????, 3 Apr. 2013.

35. Banerjee, The motive of a sheaf on the category of smooth schemes,arXiv:1311.1661v1, [math.AG], pp. 1-25, 7 Nov. 2013.

6. APPLICATIONS TO THE THEORY OF MOTIVES AND

MOTIVIC COHOMOLOGY

1. S. Saito, Some observations on motivic cohomology of arithmetic schemes, Invent.Math., v. 98 (1989), pp. 371-404.

2. V. Voevodsky, Bloch-Kato conjectures for Z/2 coefficients and algebraicMorava K-theory, Preprint, 1995, pp. 1-42, in the K-theory archive, http ://www.math.uiuc.edu/K − theory, No. 76.

3. A. A. Suslin, in: ICM 1994 in Zurich, invited talk, see item I.6 above.

4. V. Voevodsky, The Milnor Conjecture, Preprint, Dec 1996, pp. 1-55, available atthe K-theory archive, http : //www.uiuc.edu/K − theory, no. 170, Dec. 1996.

5. S. Bloch, Lecture on Mixed Motives, Proc. Sympos. in Pure Math., v. 62, Part1, AMS, Providence, 1998, pp. 329-359 (see item I-5 above).

6. M. Walker, Motivic complexes and K-theory of authomorphisms, Thesis, Univ.of Ill. Urbana-Champagne, 1996, pp. 1-137, http : //www.math.un.edu/ ∼

walker/papers.

7. C. Weibel, Products in higher Chow groups and motivic cohomology, in: ”Alge-braic K-theory, Seattle, 1997”, Proc. Symp. Pure Math., v.67, AMS, Providence,2000, pp. 305-315; see also http : //www.math.uiuc.edu/K − theory, no. 263.

8. A. Huber, Realization of Voevodsky’s motives, J. of Alg. Geometry, 9(2000), no.4, 755-799; see also http : //www.uiuc.edu/K − theory, no. 304.

9. F. Morel, Voevodsky’s proof of Milnor’s Conjecture, Bull. AMS, v. 35(1998),No. 2, see item I-12 above.

10. E. M. Friedlander, Seminaire Bourbaki 1996/97, Expos/’e 833/01-20, reprintedin the ”Handbook of K-theory”, see item I-9 above.

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11. B. Kahn, Seminaire Bourbaki 1996/97, Expos/’e 834/01-40, see item I-10 above.

12. M. Levin, Mixed Motives, AMS, Providence, 1998, see item I-11 above.

13. T. Geisser, Motivic cohomology over discrete valuation rings, Tagungsbericht39/1999, Algebraische K-theorie, Oberwolwach, 26/9-2/10/1999, pp. 12-13;http : //www.uiuc.edu/K − theory, no. 375.

14. A. Vishik, Direct summands in motives of quadrics, Preprint, 1999.

15. E. Peyre, Application of motivic complexes to negligible classes, in: ”AlgebraicK-theory. Seattle, 1999”, Proc. Symp. Pure Math., v. 67 (1999), pp. 181-211.

16. B. Kahn, Motivic cohomology of smooth geometrically cellular varieties, in: ”Al-gebraic K-theory. Seattle, WA, 1997”, Proc. Symp. Pure Math., v. 67, Amer.Math. Soc., Providence, 1999, pp. 147-174.

17. B. Kahn, The Geisser-Levine method revisited and algebraic cycles over fi-nite fields, Math. Annalen, b. 324 (2002), pp. 581-617; see also http ://www.math.uiuc.edu/K − theory, no. 438.

18. B. Kahn, Motivic cohomology and unramified cohomology of quadrics, J. Euro-pean Math. Soc., 2 (2000), pp. 145-177.

19. B. Kahn, Weight filtration and mixed Tate motives, Preprint, 2001, 4pp.

20. M. Spitzweck, Some constructions for Voevodsky’s triangulated category of mo-tives, Preprint, 2000.

21. D. Orlov, A. Vishik, V. Voevodsky, An exact sequence for KM∗

/2 with applica-tions to quadratic forms, Ann. of Math., v. 165 (2007), no. 1, pp. 1-13; see alsohttp : //www.math.uiuc.edu/K − theory, no. 454 (2000), pp. 1-15.

22. A. Suslin, V. Voevodsky, Bloch-Kato Conjectures and and motivic cohomologywith finite coefficients, in ”The arithmetic and geometry of cycles (Banif, 1998)”,NATO Sci. Ser C, Math. Phys., v. 548 (2000), pp. 117-189; see also http ://www.math.uiuc.edu/K − theory, no. 341.

23. V. Voevodsky, Motivic cohomology are isomorphic to higher Chow groups, In-tern. Math. Research Notices, 2001, no. 7, pp. 251-255; see also http ://www.math.uiuc.edu/K − theory, no. 378, 2000, pp. 1-4.

24. V. Voevodsky, Triangulated categories of motives over fields, in: V. Voevod-sky, A. Suslin, E. Friedlander, ”Cycles, Transfers and Motivic Homology The-ories”, Annals of Math. Studies, v. 143, 2000, pp. 188-238; see also http ://www.math.uiuc.edu/K − theory, no. 368, s5, 1999.

25. V. Voevodsky, Cohomological theory of sheaves with transfers, in: V. Vo-evodsky, A. Suslin, E. Friedlander, ”Cycles, Transfers and Motivic HomologyTheories”, Annals of Math. Studies, v. 143, 2001, pp. 87 - 137; see alsohttp : //www.math.uiuc.edu/K − theory, no. 368, s3, 1999.

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26. V. Voevodsky, Seattle Lectures: K-theory and Motivic cohomology, 2000, seeitem I-17 above.

27. R. Joshua, The motivic DGA, Preprint 2001, pp. 1-15, available at http ://math.uiuc.edu/K − theory, no. 470.

28. N. Yagita, Examples for the mod p motivic cohomology of classifying spaces,Trans. AMS, v. 355 (2003), no. 11, pp. 4427- 4450; see also http ://www.uiuc.edu/K − theory, no. 494, 2001, pp. 1 - 21.

29. K. Zainoullin, On rational injectivity of pretheories. Relative case, Preprint,2001, pp. 1-15, available at the K-theory archive, http : //www.uiuc.edu/K −

theory, no. 501.

30. J. Denef, F. Loeser, Motivic Igusa zeta functions, Journ. of Alg. Geom., v. 7,no. 3 (1998), pp. 505-537; see also http : //www.arXiv.org, no. AG/9803040.

31. C. Serpe, Eine triangulierte kategorie aequivarianter Motive, Preprint, Univ.Munster, SFB 478 preprintreihe, Helf 154, 2001, pp. 1-66; http : //cs.uni −muenster.de/sfb/about/publ/heft154.ps.

32. C. Serpe, A triangulated category of equivariant motives, Preprint, Univ. Mun-ster, SFB 478 preprintreihe, no. 173, 2001, pp. 1-25; http : //cs.uni −

muenster.de/sfb/publ/heft173.

33. S. Biglari, An introduction to presheaves with transfers and motivic cohomology,International Centre for Theoretical Physics, Trieste, Preprint, no. 2001/95,(2001), pp. 1-38, available at http : //www.icpt.trieste.it.

34. O. Pushin, Higher Chern classes and Steenrod operations in motivic cohomology,K-theory, v. 31 (2004), pp. 307-321; see also http : //www.math.uiuc.edu/K −

theory, no. 536, 2002, pp. 1-13.

35. B. Kahn, Sajatha R., Birational motives - I, Preprint, 2002, pp. 1-128, avail-able athttp : //www.cms.zju.edu.cn/UploadF iles/AttachFiles/20048416843137.pdf ,pp. 1-128 (an older version http : //www.math.uiuc.edu/K − theory, no. 596,pp. 1-56.

36. S. Borghesi, Stable representability of motivic cohomology, Preprint, 2002.

37. T. Geisser, Motivic cohomology over Dedekind rings, Math. Zeit., v. 248(2004),no. 4, pp. 773-794; see also http : //www.math.uiuc.edu/K − theory, no. 597,2002, pp. 1-19.

38. V. Voevodsky, Reduced power operations in motivic cohomology, Publ. Math.IHES, t. 98 (2003), no. 1, pp. 1-57; see also http : //www.math.uiuc.edu/K −

theory, no. 487.

39. V. Voevodsky, On 2-torsion in motivic cohomology, Publ. Math. IHES, t. 98(2003), no. 1, pp. 59-104, see also http : //www.math.uiuc.edu/K − theory, no.

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502.

40. V. Voevodsky, Cancellation theorem, Documenta math. Extra Volume: AndreiA. Suslin’s Sixtieth Birthday, 2010, pp. 671-685, see also E-preprint, http ://www.math.uiuc.edu/K − theory, no. 541, 2002, pp. 1-15.

41. V. Voevodsky, C. Mazza, Ch. Weibel, Notices on motivic cohomology, IAS,Princeton, 1999-2000, 230pp, 2002, see item I-18 above.

42. V. Voevodsky, Lectures on motivic cohomology, IAS, Princeton, 2000/2001,64pp., 2001, see item I-19 above.

43. E. Friedlander, A. Suslin, Work of V. Voevodsky, see item I-23 above.

44. F. Orgogozo, Isomotifs de dimension inferieure a 1, Manuscripta Math., v.115(2004), pp. 339-360; see also http : //www.dma.ens.fr/ ∼ orgogozo, pp.1 - 17.

45. F. Deglise, Interpretation motivique de la formule d’exces d’intersection, see itemII-5.11 above.

46. F. Deglise, Around the Gysin triangle II, Documenta Math., v. 13 (2008), pp.613-675, http : //www.emis.de/journals/DMJMV/vol − 13/18.ps.gz; see alsoarXiv : 0712.1604v2, [math.AG], pp. 1-65.

47. V. Guletskii, Finite-dimensional objects in distinguished triangles, Preprint,2005, pp. 1-25, J. of Number theory, (2006), to appear; see also http ://www.guletskii.org and http : //www.uiuc.edu/K − theory, no. 637, 2003,pp. 1-35.

48. C. Weibel, A road map of motivic homotopy and motivic homology theory, in”Axiomatic, enriched and motivic homotopy theory”, NATO Advanced StudyInstitute Series, Ser. II, v. 131, J. P. C. Greenlees (ed.), Elsevier Sci. Publ.,2003, pp. 385-391; see also http : //www.math.uiuc.edu/K − theory, no. 631,pp. 1-7, MR 2005e: 14033.

49. C. Mazza, Schur functors and motives, K-theory, v. 33(2004), pp. 89-106; seealso arXiv:1010.3932, [math.KT], 19 Oct. 2010, pp. 1-16; or K-theory archive,http : //www.math.uiuc.edu/K − theory, no. 641, June 2003, pp. 1-14.

50. C. Mazza, Schur functors and Motives, Thesis, Rutgers Univ. pp. 1-57, 2004, available at http : //www.math.jussieu.fr/ ∼ mazza; http ://www.carlomazza.com/wp − content/upload/phd.pdf

51. V. Voevodsky, Motives over simplicial schemes, Journ. of K-theory, 5(2010), no.01, pp. 1-38; see also K-theory archive, http : //www.math.uiuc.edu/K−theory,no. 638 (2003).

52. V. Voevodsky, On motivic cohomology with Z/ℓl coefficients, Annals of Math.??? (2011), pp. ??, see also E-prints: http : //www.math.uiuc.edu/K − theory,no. 639, June 2003, pp. 1-44, or arXiv : 0805.4430v1, [math.AG], pp. 1-45.

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53. V. Guletskii, A remark on nilpotent correspondences, Preprint, Sept. 2003, pp.1-22, available at the K-theory archive, http : //www.math.uiuc.edu/K−theory,no. 651.

54. Th. Geisser, Preprint, 2003, see item I.32 above.

55. Y. Takeda, Sugaku Expositions, v. 16, (2003), no. 2, pp. 207-224, see item I-26above.

56. J. Nicaisse, Relative motives and theory of quasi-finite fields 1, Preprint, 2004,pp. 1-31, available at http : //www.arXiv.org, no. math.AG/0403160 orhttp : //www.wis.kuleuven.ac.be/algebra/artikels/elimination.pdf

57. A. Suslin, On the Grayson spectral sequence, Trudy Mat. Inst. Steklova, t.241, no. 2, Number Theory, Algebra and Algebraic Geometry, Collected papersdedicated to 80th birthday of academician I. R. Shafarevich, pp. 218-253, Nauka,Moscow, 2003 (English translation in: Proc. Steklov Math. Inst. 2003, no.2 (241), pp. 202-237); http : //www.mathnet.ru/eng/tm/241/p218, see alsohttp : //www.math.uiuc.edu/K − theory, no. 588, 2002, pp. 1-48.

58. C. Haesemeyer, J. Hornbostel, Motives and etale motives with finite coef-ficients, K-theory, v. 34 (2005), no. 3, pp. 195-207; see also http ://www.math.uiuc.edu/K − theory, no. 678.

59. F. Deglise, Motifs generiques, Preprint, Feb. 2005, pp. 1-55, available at http ://math.univ−paris13.fr/ ∼ deglise/preprint.html, or K-theory archive, http ://www.math.uiuc.edu/K − theory, no. 690, 2005, pp, 1-55.

60. B. Kahn, Birational motives, I, Preprint, 2004, pp. 1-56, available at http ://www.math.jussieu.fr/ ∼ kahn

61. Theory of Motives, homotopy theory of varieties and dessins d’enfants, No-tices of the AIM Workshop, Palo Alto, April, 2004, available at http ://www.aimath.org/WWN/motivesdeissins//motivesdessigns.pdf (especiallycontributions by J. R. Jardine, B. Kahn, M. Levine, O. Roendigs,...).

Open questions, ed. O. Ronding.

62. J. Wildeshaus, The boundary motive: definition and basic properties, Compo-sitio Math., 142(2006), 631-656, http : //journals.cambridge.org/production/action/cjoGetFulltext?fulltextid = 438965; see also http : //www.math.uiuc.edu/K − theory, no. 704; or wwwmath1.uni − muenster.de/sfb/about/publ/heft344.ps

63. J. Wildeshaus, On the boundary motive of a Shimura variety, see also item 2-34above.

64. A. Nenashev A., K. Zainoulline, Motivic decomposition of relative cellular spaces,Preprint, Sept., 2004, pp. 1-24, available at the K-theory archive http ://www.math.uiuc.edu/K − theory, no. 710; see also arXiv : math.AG/0407082(p.4).

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65. R. Joshua, Motivic E∞-algebras and motivic DGA, Preprint, 2007, pp. 1-29,available at http : //www.math.ohio − state.edu/ ∼ joshua.1/mdga17.pdf .

66. A. Del Pardone, C. Mazza, Schur-finiteness and nilpotency, Comptes RendusAcad. Sci., Paris, t. 341(2005), pp. 283-286; see also arXiv:1010.3922v1,[math.AG], Oct. 2010.

67. S. Biglari, Motives of a reductive group, Thesis, Univ. of Leipzig, 2004, pp. 1-57,available at http : //www.math.uni − leipzig.de/ ∼ huber/preprints.html, toappear, see also Summary, www.docstoc.com/docs/2319854/Summary − of −

the − Dissertation, 2pp.

68. F. Deglise, Motivic interpretation of excess intersection formula and ramifiedcase, see item II-5.13 above.

69. A. Huber, B. Kahn, The slice filtration and mixed Tate motives, Composit.Math., v. 142 (2006), pp. 907-936, see also http : //www.math.uiuc.edu/K −

theory, no. 719.

70. A. Huber, Slice filtration on motives and Hodge Conjecture, MathematischeNachrichten, v.??? (2007), see also http : //www.math.uiuc.edu/K − theory,no. 725, pp. 1-12.

71. G. Powell, Motivic cohomology of Cech objects - after Yagita and Voevodsky,Preprint, 2005, pp. 1-21, available at http : //www.math.univ− paris13.fr/ ∼

powell /documents/2005/cech.pdf .

72. B. Kahn, J. P. Moore, C. Pedrini, On the trancedental part of the motive of asurface, in ”Algebraic Cycles and Motives”, vol. 2, Lect. Notes Lond. Math.Soc., vol. 344, 2007, pp. 143-202; see also http : //www.math.uiuc.edu/K −

theory, no. 759, Oct. 2005.

73. F. Deglise, Finite correspondences and transfers over a regular base, in ”Al-gebraic Cycles and Motives”, v. 1, Lect. Notes in Math., v. 343, 2007,pp. 138-205; see also http : //www.math.u − paris13.fr/ ∼ deglise, orhttp : //www.math.uiuc.edu/K − theory, no. 765, Jan. 2006.

74. E. Friedlander, Motivic complexes of Suslin-Voevodsky, Seminaire Bourbaki, an-nee 1996/97, expose 836; reprinted in the ”Handbook of the K-theory, v2, pp.1081-1104, see item I.9 above.

75. M. Levine, Mixed Motives, in ”Handbook of K-theory”, eds. L. Fried-lander and D. Grayson, Springer, 2005, pp. 429-522; see also http ://www.math.neu.edu/ ∼ levine.

76. Th. Geisser, Motivic cohomology, K-theory and topological cyclic homology, in”Handbook of K-theory”, E. Friedlander and D. Grayson, eds,, Springer, 2005,v. 1, pp. 193-234; see also http : //www.math.usc.edu/ ∼ geisser/hb.ps, 2003,pp. 1-40.

77. Scholbach, Geometriche Motiven und h-topologie, Math. Zeit., 2011;

33

see also http : //www.math.uni − leipzig.de/ ∼ huber/preprints/ orpublic endfassung.pdf , pp. 1-68.

78. L. Barbieri-Viale, On the theory of 1-motives, in ”Algebraic cycles and motives”,v. 1, London Math. Soc. Lect. Notes Ser., v. 343 (2007?), pp. 55-101, see itemI-45 above.

79. Zh. Nie, Karoubi’s construction of Motivic cohomology operations, Diss.,SUNY at Stony Brook, Aug. 2005, pp. 1-99; available at http ://mosaic.math.tamu.edu/ ∼ nie/preprints/thesis.pdf .

80. F. Deglise, Motifs generiques, Preprint, 2005, pp. 1-54, available at http ://www.math.u − paris13.fr/ ∼ deglise.

81. F. Ivorra, Realization ℓ-adique des motifs triangules geometriques. I, Docu-menta Math. 12(2007), pp. 607-671, see also http : //www.math.jussieu.fr/ ∼

fivorra/RealAdiqueA; or http : //www.math.uiuc.edu/K − theory, no. 762.

82. F. Ivorra, Realization ℓ-adique des motifs triangules geometriques II,Prepublication, 2005, pp. 1-44, available at http : //www.math.jussieu.fr/ ∼

fivora/RealAdiqueB.

83. F. Ivorra, Realization l-adique des motifs mixtes, These, Univ. Paris VI, availableat http : //www.math.jussieu.fr/ ∼ fivorra/These.pdf .

84. F. Ivorra, Realization ℓ-adique des motifs mixtes, Comptes Rendus Acad. Sci,Paris, t. 342 (2006), pp. 505 - 510.

85. F. Ivorra, Levine’s motivic comparison theorem revisited, available at http ://www.math.uiuc.edu/K − theory, no. 788, 2006, pp. 1-40.

86. M. Bondarko, Enhancement for the triangulated category of motives realizations,truncations, weight filtrations, and motivic descent spectral sequence, Preprint,Jan. 2006, pp. 1-44, available at http : //www.arXive.org, math.AG/0601713.

87. V. Guletskii, Zeta functions in tringulated categories, E-print, 2006, pp. 1-16,available at http : //www.arXiv.org, AG/0605040.

88. J. Scholbach, Geometrical motives and the h-topology, Preprint, 2005, pp. 1-26,available at http : //www.math.iuuc.edu/K − theory, no. 792,

89. N. Spitzweck, Motivic approach to limit sheaves, ”Geometric Methods in Algebraand Number Theory”, eds. F. Bogomolov and Y. Tschinkel, Progress in Math.,Progress in Math., v. 235 (2005), Birkhauser, pp. 283 -302; see also http ://www.springerlink.com/index/4572w5315204216.pdf

90. L. Barbieri-Viale, B. Kahn, On the derived category of 1-motives, E-print, 214pp., arXiv:1009:1900v1, [math.AG], 9 Sept. 2010; earlier ver-sions: http : //www.ihes.fr/PREPRINT/2007/M/M − 07 − 22.pdf , http ://www.arXiv.org : 0706.1498, [math.AG], or http : //www.math.uiuc.edu/K−

theory, no. 851.

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91. A. Bondarko, Lecture at the Hodge theory conference, Venice, June 2006, pp.1-11, available at https : //convegni.math.unipd.it/hodge/slides/bondarko.pdf .

92. J. Riou,Realization functeurs, Expose a l’Ecole d’Ete Franco-Asiatique ”La Geometriealgebrique et la nombre theorie, ”Autour des motives”, a IHES, 2006, pp. 1-44;available at http : //www.math.u − psud.fr/ ∼ rion/doc/realizations.pdf , orhttp : //ihes.fr/IHES/Scientifique/asie/textes/realizations − riou.pdf

93. Riou, Realization functors, Preprint, pp. 1-20, 2006, available at http : //www.math.u − psud.fr/ ∼ riou/doc/realizations.pdf .

94. I. Sou, Notice on A. B. Goncharov- Y. Manin articles [G-M2], pp. 1-14; http ://ismael.sou.free.fr/boston/Gon − Man − motives3.pdf

95. A. Beilinson, A. Otwinowska, V. Vologodsky, Motivic sheaves over a curve,Lecture at the Hodge theory conference, Venice, 2006, pp. 1-40, availabe athttp : //convergni.unipd.it/hodge/slides/otwinowska.pdf .

96. F. Lecomte, N. Wach, Le complexe motivique de De Rham, E-print, Jan. 16,2007, available at http : //www.arxiv.org, math.NT/07011443, pp. 1-10.

97. J. Ayoub, The slice filtration on DM(k) does not preserve geometricmotives, available at http : //www.math.jussiu.fr/ ∼ ayoub/AppendixAnnette/appendix − hodge − mn.pdf , pp. 1-4.

98. L. Barbieri-Viale, B. Kahn, A note on relative duality for Voevodsky mo-tives. Tohoku Math. J., v. 60 (2008), no.3, pp. 349-356, see also http ://www.math.uiuc.edu/K − theory, no. 817 or http : //www.arXive.org, no.math.AG/0701782.

99. S. Borghesi, Cohomology operations and algebraic geometry, Geometryand topology monographs, v. 10(2007), 75-115. available at http ://www.warwick.ac.uk/gtm/2007/10/gtm− 2007− 10− 004s.pdf ; see also http ://arxiv.org, no. 0903.4360v1 [math.AT].

100. M. V. Bondarko, Explicit generation for mixed motives, Preprint, 2007, pp. 1-6,available at http : //www.arXiv.org, no. math.AG/0703499.

101. F. Ivorra, Realization ℓ-adique des motifs mixtes, Expose, Seminaire de Theoriedes Numbres, Bordeaux, Jan. 2006, pp. 1-60, available at http : //www.uni −due.de/ ∼ hm0035/ExposeBordeaux.pdf ,

102. F. Ivorra, Realization ℓ-adique et une equivalence motivique, Lectures atSeminaire de Geometrie Algebrique de Rennes, Fall, 2006, pp. 1-88, availableat http : //www.uni − due/de/ ∼ hm0035/ ExposeRennes.pdf .

103. A. Chatzistamatiou, Motivische Kohomologie von Komplement von Konsella-tion affine Raume, Duisburg, Essen, Math., 2006, 130pp., http : //deposit.d −

ub.de??/egi − bin/dokserv?

35

104. F. Ivorra, ℓ-adic realization of triangulated motives over a noetherian sep-arated scheme and a motivic equivalence, http : //www.uni − due.de/ ∼

hm0035/MFO.pdf

105. D.-Ch. Cisinski, F. Deglise, Local and stable homological algebra in Grothendieckabelian categories, Homology theory, Homotopy theory and applications, v. 11(2009), pp. 219-260. See also E-print, Dec. 2007, pp. 1-40, http : //arXiv.org,no. 0712.3296 [math.AG].

106. D.-Ch. Cisinski, F. Deglise, Triangulated categories of mixed motives, E-print, pp. 1-229, arXiv:0912.2110v2, [math.AG], 13 Dec. 2009; or http ://hal.archives−ouvertes.fr/docs/00/ 44/09/08/PDF/DM.pdf , version 1, Dec.13, 2009, pp. 1-229.

107. F. Deglise, Around the Gysin triangle I, E-print, April, 2008, pp. 1-37,arXiv:0804.3415; an older version see also http : //www.math.uiuc.edu/K −

theory, no. 764, Jan. 2006, pp. 1-32.

108. F. Deglise, Around the Gysin triangle II, Documenta Math., v. 13 (2008), pp.712-786; see also arXiv : 0712.1604v2, [math.AG], pp. 1-64.

109. F. Ivorra, Rapport sur les travaux efectues, Mars, 2007, pp. 1-18, available athttp : //www.uni − due.de/ ∼ hm0035/RapportT ravaux.pdf .

110. A. Krishna, M. Levine, Additive Chow groupsm of schemes, Journ. furdie reine und angew. math., June 2008, no. 619, pp. 75-140;see also http : //www.arXiv.org, no. 0702138 [math.AG] or http ://www.math.neu.edu/ levine/publ/AdditiveChow.pdf

111. M. V. Bondarko, Weight strucures vs t-structures: weight filtrations, weight spec-tral sequences and weight complexes (for motives and in general), Journ. of theK-theory, v. 3, no. 3, 2010, pp. 387-504; see also http : //www.arXiv.org, no.0704.4003v8 [math.KT], 17 Jan. 2011 pp. 1-122; or earlier version see also http ://www.euler−foundation.org/wp−content/uploads/2007/04/motlong.pdf , pp.1-72.

112. M. V. Bondarko, Artin’s vanishing for torsion motivic homology, numericalmotives form tannakian category, E-print, Nov. 2007, pp. 1-44, available athttp : //www.arXiv.org, no. arXiv:0711.3918v1, [math.AG].

113. J. Wildeshaus, Pure motives, mixed motives and extensions of mo-tives accociated to singular surfaces, Preprint, June, 2007, pp. 1-36, available at http : //www.math.uiuc.edu/K − theory, no. 856,or http : //www.arxiv.org, arXiv:0706.4447, [math.AG], or http ://www.crm.es/Publications/07/Pr758.pdf .

114. S. Kelly, Homology of schemes, Master 2 thesis, Univ. Paris XI, Sept.2007, pp. 1-72, http : //www.math.u − bordeaux.fr/ALGANT/documents/theses/kelly07.pdf or http : //www.algant.eu/documents/theses/kelly07.

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115. P. Bronsan, R. Joshua, Cohomology operations in motivic, etale and de Rham-Witt cohomology, http : //www.math.ohio − state.edu/ ∼ joshua/coh −

ops.new.pdf , pp. 1-???.

116. H. Esnault, M. Levine, Tate motives and the fundamental group, E-preprint,Aug. 2007, pp. 1-62, available at http : //www.arXiv.org, 07084034, v. 1,[math.AG].

117. V. Voevodsky, Motivic Eilenverg-MacLane spaces, E-preprint, pp. 1-99,arXiv:0805.4432v2, [math.AG], 29 Sept. 2009; an older version in the K-theoryarchve, http : //www.math.uiuc.edu/K − theory, no. 864 pp. 1-76, 2007.

118. A. Asok, B. Doran, F. Kirwan, Yang-Mills theory and Tamagawa numbers:the fascination with unexpected links in mathematics, Presidential address,Bull. London Math. Soc., v. 40 (2008), pp. 533-567; see also E-printhttp : //www.arxiv.org, no. arxiv:0801.4733, [math.AG];

119. A. Asok, B. Doran, F. Kirwan, Equivariant motivic cohomology and quotients,In preparation (2007).

120. A. Chatzistamatiou, Motivic cohomology of the complement of hyperplanearrangements, available at http : //www.uni − duisburg − essen.de/ ∼

mat903/preprints/

121. T. Hiranouchi, S. Mochizuki, Deforming motivic theories I. Pure weight perfectModules on divisorial schemes, Preprint, 2008, pp. 1- 35, available at http ://www.math.uiuc.edu/K − theory, no. 876?.

122. J, Wildeshaus, Chow motives without projectivity, Compos. Math., 145(2009),1196-1226; see also http : //arxiv.org: no. 0806:3380v1, [math.AG], pp. 1-36(2008); or http : //www.math.iuic.edu/K − theory, no. 899.

123. J. Wildeshaus, f -categories and Tate motives, E-print, Oct. 10, 2008, pp. 1-13; available at http : //www.arxive.org, no. 0810.1677, [math.AG], or in theK-theory archive http : //www.math.uiuc.edu/K − theory no. 913.

124. V. Vologodsky, The Albanese functor commutes with the Hodge realization,E-print, Sept. 18, 2008, pp. 1-18, available at http : //www.arXiv.org, no.0809.2830, [math.AG].

125. F. Lecomte, Realization de Betti des motives de Voevodsky, Comptes RendusAcad. Sci. Paris, t. 346 (2008), no. 19-20, pp, 1083-1086.

126. J. Wildeshaus, Notes on Artin-Tate motives, Preprint, pp. 1-18, Nov. 27, 2008,available at the K-theory archive: http : //www.math.uiuc.edu/K − theory, no.918, and at arXiv : 0811.4551, [math.AG].

127. N. Yagita, Coniveau filtration of cohomology of groups, Proc. of the Lon-don Math. Soc., v.101 (2010), no. 3, pp. 179-206; see also http ://hopf.math.purdue.edu/Y agita/coniveaufilt.pdf , pp. 1-36, 2008.

37

128. Z. Nie, Karoubi’s construction for motivic cohomology operations, Amer.J. Math., 130(200?), pp. 713-762; see also http : //www.arXiv.org, no.math.AG/0603458.

129. C. Bertoline, C. Mazza, Biextension of the 1-motives in Voevodsky category ofmotives, Internat. Math. Research Notices, Sep. 14, 2009, pp. 3747-3757; seealso http : //www.arXiv.org, no. 0901.0331v1, [math.AG], 5 Jan., 2009, pp.1-8.

130. M. V. Bondarko, Differential graded motives: weight complex, weight filtra-tion and spectral sequences for realizations: Voevodsky versus Hanamura, Journ.Math. Jussieu, 8(2009), no.1, pp. 39-97.

131. J. Ayoub, L. Barbieri-Viale, 1-motivic sheaves and the Albanese functor, Jour.Pure and Appl. Algebra, v. 213, no. 5, May 2009, pp. 809-839; see alsohttp : //www.arXiv.org, no. 0607.738v2, [math.AG], Oct. 2008, pp. 1-54.

132. F. Deglise, Motifs generiques, Rend. Semin. Mat. Univ. Padova, t. 119 (2008),pp. 173-244.

133. F. Deglise, Modules homotopiques, Docum. math., v. 16 (2011), pp. 411-455,(13.dvi); an earlier version: E-print, arXiv : 0904.4747v1, [math.AG], pp. 1-60,30 Apr. 2009.

134. I. A. Panin, S. A. Yagunov, Duality theorem for motives, Algebra and analysis, t.21(2009), no. 2, 309-315; engl. transl.: St. Petersburg Math. J., vol. 21(2010),no. 2, pp. 309-315.

135. T. B. Williams, Equivariant motivic cohomology, Preprint, pp. 1-10, 2009, http ://www.math.stanford.edu/ ∼ williams/motivicRSS.pdf

136. T. B. Williams, The equivariant motivic cohomology of varieties of long ex-act sequences, Thesis, Stanford, 2010, pp. 1-134, www − bcf.usc.edu/ ∼

tbwillia/Thesis.pdf .

137. A. Bourthier, Realisation de de Rham des motifs de Voevodsky, E-preprint, pp.1-41, arXiv:0909.5376v1, [math.AG], 29 Sept., 2009.

138. J. Ayoub, Note sur les operations de Grothendieck et la realizations de Betti,J. Inst. Math. Jussieu, 9(2010), no. 2, 225-263; an earlier version: http ://user.math.uzh.ch/ayoub, 2009, pp. 1-25.

139. F. Lecomte, N. Wash, Realisations des complexes motiviques de Voevodsky, E-print, http://www.math.uiuc.edu/K-theory, no. 99? Feb. 2011, pp. 1-28; anolder version: 30 Nov. 2009, pp. 1-25, arXiv:0911.5611v1, [math.NT].

140. Chenghao Chu, Representing cohomology theories in the triangulated cat-egories of motives, Thesis, Northwestern U., 2008, pp. 1-72, http ://www.docstoc.com/46998195/Representing − cohomology − theories... http ://grin.com/en/doc/250507/representing − cohomology − theories− in− the−triangulated − category − ..

38

141. Chenghao Chu, Morphic cohomology and singular cohomology of motives overthe complex numbers, Topology and its appl., v, 156 (2009), no. 17, pp. 2812-2831.

142. T. Geisser, On Suslin’s singular homology and cohomology, E-print, 7 Dec. 2009,pp. 1-25, available at arXiv:0912.1168v1, [math.AG].

143. T. Geisser, Parshin’s conjecture and motivic cohomology with compact supports,E-print, 31 Jan. 2010, pp. 1-14, availabe at arXiv:1002.0105v1, [math.KT].

144. M. V. Bondarko, Z[1/p]-motivic resolution of singularities, Composit. Math., v.147 (2011), no. 5, pp. 1434-1446; see also arXiv:1002.2651v1, [math.AG], pp.1-18, 15 Feb. 2010.

145. J. Wildeshaus, f -categories, tours et motifs de Tate, Comp. Rend. Acad. Sci.Paris, ser. Mathematique, t. 347 (2009), no. 23, pp. 1337-1347.

146. J. Wildeshaus, Boundary motive, relative motives and extension of motives, E-print, 45pp., 12 April, 2010, arXiv:1004.1631.

147. J. Ayoub, L’algebre de Hopf et le groupe de Galois motiviques d’un corps decharacteristique nulle, E-print, May 23, 2010, pp. 1-177, available at K-theoryarchive, http://www.math.uiuc.edu/K-theory, no. 963.

148. F. Deglise, Orientable homotopy modules, E-print, 21 May, 2010,arXiv:1005.4187v1, [math.AG], pp. 1-28; http : //hal − archives −

ouvertes.fr/docs/00/48/59/21/PSmhtpo.ps.

149. M. Spitzweck, Derived fundamental groups for Tate motives, E-print, May, 2010,pp. 1-25?, arXiv:1005.2670.

150. M. Bondarko, Motivically functorial coniveau spectral sequences; direct sum-mands of cohomology of function fields, Documents math., Extra vol.: An-drei A. Suslin sixtieth birthday, 2010, pp. 33-117, an earlier version http ://www.arXiv.org, ???

151. T. Geisser, On Suslin’s singular homology and cohomology, Documenta Math.,Extra Vol. dedicated to Andrei Suslin sixtieth birthday, 2010, pp. 223-250.

152. A. S. Merkuriev, A. A. Suslin, Motivic cohomology of the simplicial motive of aRost variety, Journ. Pure and Appl. alg., 214(2010), 2017-2026.

153. M. V. Bondarko, Weight structures and motives; comotives, coniveau and Chow-weight spectral sequences, and mixed complexes of sheaves: a survey, E-print,pp. 1-23, iarXiv:0903.0091v4, [math.AG], 20 Sept. 2010.

154. B. Kahn, Somekawa’s K-group and Voevodsky’s Hom group, E-print, pp. 1-15,available at arXiv:1009.4554v1, [math.AG], 23 Sept. 2010; or k-theory archive,http : //www.math.uiuc.edu/K − theory, no. 973, 23 Sept. 2010.

155. D. Hebert, Structure de poids a la Bondarko sur les motives de Beilinson, E-print,pp. 1-15, arXiv:1007.0219v3, [math.AG], 21 Oct., 2010.

39

156. F. Deglise, These d’habilitition a diriger des recherches. Memoire de synthese,Juin 2010, pp. 1-48, http : //math.univ − paris13.fr

157. F. Deglise, Beilinson motivies and the six functors formalism, Preprint, 2010, pp.1-6, http : //www.math.univ − paris13.fr/ ∼ deglise.

158. F. Deglise, Motifs mixtes arithmtiques, Preprint, 2010, pp. 1-7, http ://www.math.univ − paris13.fr/ ∼ deglise.

159. A. Holmstrom, J. Scholbach, Arakelov motivic cohomology I, E-print,arXiv:1012.2523v1, [math.NT], 12 dec. 2010.

160. A. Holmstrom, Arakelov motivic cohomology, Thesis, Cambridge U., 2010, avail-able at andreasholmstrom.org/thesis.pdf

161. A. Holmstrom, Arakelov motivic cohomology and zeta values, Oberwolfach, 2010,3pp.

162. A. Banerjee, Tensor structure on smooth motives, E-print, pp. 1-???,arXiv:1004.1491v2, [math.AG], [math.KT], 9 April 2010.

163. A. Banerjee, Tensor functor from smooth motives to motives over a base, E-print,pp. ??? arXiv:1111.3718v??, [math.AG], [math.KT], ??? Nov. 2011.

164. L. Positselski, Artin-Tate motivic sheaves with finite coefficients over smoothvarieties, E-print, http://www.math.uiuc.edu/K-theory, no. 991, pp. 1-18, Jan.17, 2011; an earlier version: arXiv:1012.3735, [math.AG], 17 Dec. 2010.

165. F. Lecomte, N. Wash, Realisations des complexes motiviques de Voevodsky, E-print, http://www.math.uiuc.edu/K-theory, no. 998??, Feb. 2011, pp. 1-28; anolder version: 30 Nov. 2009, pp. 1-25, arXiv:0911.5611v1, [math.NT].

166. R. Ayoub, La realisation etale et les operations de Grothendieck, Preprint,Jan. 9, 2011, pp. 1-110, available at the K-theory archive, no. 989, http ://www.math.uiuc.edu/K − theory.

167. J. Ayoub, The n-motivic t-structures for n = 0, 1, 2, Advances in Math., v. 226,(2011), no. 1, pp. 111-138; see also http : //www.math.uiuc.edu/K − theory,no. 938, Dec. 2009.

168. V. Vologodsky, Some remarks on the integral Hodge realization of Voevodskymotives, E-print, pp. 1-9, arXiv:1102.0579v1, [math.AG], 2 Feb., 2011.

169. F. Deglise, Coniveau filtration and mixed motives, E-print, pp. 1-25,arXiv:1106.0905v1, [math.AG], 5 June, 2011.

170. J. Riou, Steenrod operations, in ”Motives and Milnor conjectures”, lecturesat Summer school, Jussieu, June 14 and 16, 2011, 83pp., available at http ://www.math.u − psud.fr/ riou.

171. S. Kelly, Motives and Milnor conjecture Notices, Day I, pp. 1-14; notices −

2011.institut.math.jussieu.fr/notes/Day − 1.pdf

40

172. G. Garkusha, I. Panin, K-motives of algebraic varieties, E-print, pp. 1-50, 1Aug. 2011, arXiv:1108.0375, [math.AG].

173. U. Choudhury, Motives of Deligne-Mumford stacks, Advances in Math., 231(2012), no. 6, pp. 3094-3117, see also arXiv:1109.5288v1, [math.AG], 24 Sep.2011. pp. 1-22 or http : //www.math.uiuc.edu/, K−theory, no. 1012, pp. 1-22,Sep. 28. 2011.

174. B. Williams, Intermedian equivariant topologies, Preprint, 2011, pp. 1-21??,http : //www − bcfusc.edu/ ∼ tbwillia/IntermedianEquivariantTopologies.pdf .

175. B. Williams, Motivic cohomology of Stiffel varieties, Preprint, pp, 1-21, April,2011, http : //math.stanford.edu/ ∼ williams/MotivicCohoStifel.pdf .

176. B. Williams, Generalities on motivic cohomology, Preprint, pp. 1-5, 2011, http ://math.stanford.edu/ ∼ williams/Generalities.pdf .

177. B. Williams, The Gm-equivariant motivic cohomology of Stiffel varieties, E-print,arXiv:1203.5584, [math.AG], pp. ???, Mar. 26, 2012.

178. F. Ivorra, Triangulated motives over noetherian separated schemes, in: Motivicintegration and its interractions with model theory, eds. Clukers R., Nacaise J.,Sebag J., vol. II, London math. soc. lect. notes ser., v. 383, 2011, pp. 108-177.

179. E. Shinder, On motives of algebraic groups associated to a division algebra,arXiv:1202.3090v1, [math.AG], 14 Feb. 2012, pp. 1-24.

180. M. V. Bondarko, A fat hyperplane section weal Leschetz and Barth-type theo-rems, E-print, arXiv:1203.2595, [math.AG], pp. 1-21, Mar. 12, 2012.

181. A. Asok, Rationality problems and conjectures of Milnor and Bloch-Kato, E-print, arXiv:1203.4022, [math.AG], pp. 1- 15, Mar. 19, 2012.

182. Nguyen Le Dang Thi, Embedding of category of Chow-Witt correspondences intogeometric stable A1-derived category over a field, E-print, arXiv:1204.2787v7,[math.AG], 17 Aug., 2012, pp. 1-15.

183. J. Scholbach, Arakelov motivic cohomology II, E-print, arXiv:1205.3890,[math.AG], pp. 1-28, May 17, 2012.

184. J. Ayoub, L. Barberi-Viale, Nori ℓ-motives, E-print, arxiv:1206.5923, [math.AG],pp. 1-35, June 26, 2012.

185. J. Ayoub, 2-motives, Abstract, pp. 1-3,http : //user.math.uzh.ch/ayoub/Other − PDF/2 − motives.pdf .

186. M. Spitzweck, A commutative P1-spectrum representing motivic cohomologyover Dedekind domain, E-print, arXiv:1207.4078v2, [math.AG], July 19, 2012,pp. 1-48.

187. G. Faltings, Motivic logarithm for curves, in: J. Stix (ed.), Arithmetic of funda-

41

mental groups, Springer, 2012, pp. 107-125.

188. B. Kahn, Classes de cycles motiviques etales, Algebra and number theory, v.6(2012), no. 7, 1367-1407; msp.org/ant/2012/6− 7/ant− v6− n7− p04− p.pdf

189. U. Choudhury, J. Skowera, Motivic decomposition for relative geometrically cel-lular stacks, Preprint, 2012, pp. 1-8, http : //user/math.uzh.ch/skowera/cell−staks.pdf

190. F. Lecomte, N. Wach, Realization de Hodge des motives de Voevodsky, Manuscr.Math., v. 141 (2013), no. 3-4, pp, 663-697.

191. S. Kondo, S. Yasuda, The Riemann-Roch theorem without denominators in mo-tivic homotopy theory, http : //db.ipmu.jp/ipmu/sising/724.pdf pp. ????

192. R. Joshua, Comparison of motivic and classical operations in mod-ℓl motiviccohomology, http : //www.math.osu.edu/ ∼ joshua.1/coh − ops15/pdf .

193. M. Bondarko, On weight for relative motives with integral coefficients, E-print,arXiv:1304.2335v1, [math.AG] and [math.KT], April 8, 2013, pp. 1-24.

194. B. Guillou, Ch. Weibel, Unstable operations in etale and motivic cohomology,E-print, arxiv:1301.0872v1, [math.AG], 5 Jan. 2013, pp. 1-???.

195. G. Garkusha, I. Panin, The triangulated category of K- motives DK(k), E-print,arXiv:1302.2163v1, [math.AG], Feb 8, 2013, pp. 1-???.

196. J. Heller, M. Voineagu, P. A. Ostvaer, Equivariant cycles and cancela-tions in motivic cohomology, http : //www2.math.uni − wuppertal.de/ ∼

heller/ECpost.pdf 2013, pp. 1-56; an earlier version: E-print, arXiv:1304.5867,[math.AG], 22 Apr, 2013, pp. 1-19??, 55kb.

197. M. Bondarko, V. Sosnilo, Non-commutative localiztions of additive cate-gories and weight structures: applications to birational motives, E-print,arXiv:1304.6059v2, [math.AG], [math.KT], [math.CT], 29 April, 2013, pp. 1-???

198. S. Kelly, Triangulated categories of motives in positive characteristic, Thesis,Oct. 2012, Univ. Paris 13, E-print, arXiv:1305.5349v1, [math.AG], May 23,2013, pp. 1-159.

199. D.-C. Cisinski, F. Deglise, Etale motives, E-print, arXiv:1305.5361v1,[math.AG], May 23, 2013, pp. 1-??? 109kb.

200. T. Kohrita , On some negative motivic homology groups, arXiv:1308.0935v1,[math.AG], 17pp, Aug. 8, 2013. pp. 1-???.

201. I. Iwanari, Mixed motives and quotient stacks: abelian varieties, E-print,arXiv:3175v3, [math.AG], [maht.NT], 28 Aug, 2013, pp. 1-50, 65Kb.

202. S. Enright-Ward, The Voevodsky motive of a rank one semiabelian varoety, PhDThesis, E-print, arXivi:1307v1, [math.AG], July 17, 2013, pp. 1-176, 96Kb.

42

203. Milne J., Ramachandran ??, Motivic complexes and special values of zeta func-tions, arXiv:1311.3166v1, [math.AG], 13 Nov. 2013, pp. 1-41.

7. APPLICATIONS TO THE MOTIVIC HOMOTOPY THEORIES

OF ALGEBRAIC VARIETIES AND SCHEMES

1. Ye. Nisnevich, 1989, see title II-1.3 above.

2. J. R. Jardine, The Leray spectral sequence, Journ. of Pure and Appl. Algebra,61(1989), No. 2, 186 - 196.

3. J. R. Jardine, Generalized Etale Cohomology, see title I-7 above.

4. P. G. Goerss, J. F.Jardine, Localization theories for simplicial presheaves, Canad.J. Math., 50(1998), pp. 1048-1089.

5. F. Morel, Voevodsky’s proof of Milnor’s Conjecture, see title I-12 above.

6. B. Kahn, Seminaire Bourbaki, 1996/97, see item I-10 above.

7. V. Voevodsky, The Milnor Conjecture, see item II-6.4 above.

8. V. Voevodsky, Seattle lectures on K-theory and Motivic cohomology, see itemI-17 above.

9. F. Morel, Suite spectrale de Adams et invariants cohomologique des formesquadratiques, Comptes Rendus Acad. Sci. Paris, t. 328, No. 1 (1999), p.963-968.

10. F. Morel, Theorie homotopique des schemas, Asterisque, t. 256 (1999), 130pp.

11. F. Morel, Suites spectrales d’Adams et conjectures de Milnor. Preprint (pre-liminary version), pp. 1-30, 2000, available at http : //www.mathematik.uni −muenchen.de/ ∼ morel.

12. V. Voevodsky, A1-homotopy theory, in: ICM 1998, Berlin, see item I-13 above.

13. Po Hu, On the Picard group of A1-stable homotopy category, Topology, 44(2005),pp. 609-640; see also http : //www.math.wayne.edu/ ∼ po;

14. Po Hu, Notes on E∞-specra in the category of schemes, Preprint, U. Chicago,2000.

15. G. Vezzosi, Brown-Peterson spectra in stable A1-homotopy theory, Rend.Sem. Mat. Univ. Padova, v. 106 (2001), pp. 47-64, see also http ://www.math.uiuc.edu/K − theory, no. 400.

16. M. Hovey, Spectra and symmetric spectra in general model categories, Journ. ofPure and Appl. Algebra, v. 165 (2001), no. 1, pp. 63-127 (see an earlier versionat http : //www.math.uiuc.edu/K − theory, no. 402, June, 2000, pp. 1-45).

43

17. D. Dugger, Universal homotopy theories, Adv. Math., v. 164 (2001), no. 1,144-176, see also math.AT/0007070 v1, 2000, pp. 1- 25.

18. J. F. Jardine, Motivic homotopy theory of presheaves, Preprint, 1999,pp. 1-12, available at http : //www.math.uwo.ca/ ∼ jardine/papers;http://sciencestage.com/d/1441188/motivic-homotopy-theory-of-presheaves.html

19. J. F. Jardine, Motivic symmetric spectra, Documenta Mathematica, b. 5 (2000),pp. 445-552; see also eprint http : //www.math.uiuc.edu/K − theory, no. 448,2000, pp. 1-107.

20. Jardine J. F., Presheaves of symmetric spectra, Journ, Pure and Applied Algebra,v. 150 (2000), pp. 137-154.

21. F. Morel, The homotopy t-structures of the stable homotopy category ofschemes, Preprint, pp. 1-49, 2000, available at http : //www.mathematik.uni −muenchen.de/ ∼ morel.

22. V. Voevodsky, Seattle lectures, in: Proc. Symp. Pure Math., v. 67 (2000), seetitle I,16 above.

23. V. Voevodsky, Homotopy theories of simplicial scheaves in completely decom-posed topologies, Journ. of Pure and Appl. algebra, v. 214 (2010), pp. 1384-1394; see also http : //www.math.uiuc.edu/K − theory, no. 443, pp. 1-34??; orarXiv:0805.4578v1, [math.AG], pp. 1-33.

24. V. Voevodsky, Unstable motivic homotopy categories in Nisnevich and cdh-topologies, J. of Pure and Appl. Algebra, 214(8) (2010), pp, 1399-1406;see also arXiv:0805.4576v1, [math.AG], 29 May, 2008, pp. 1-19; or http ://www.math.uiuc.edu/K − theory, no. 444, pp. 1-22, Aug. 2000.

25. F. Morel. V. Voevodsky, A1-Homotopy Theory of schemes, Publ. Math. IHES,v. 90 (2000), pp. 45-142, an earlier version in the K-theory preprint archive:http : //www.math.uiuc.edu/K − theory, no. 305, 1998.

26. Borghesi S., Algebraic Morava K-theories and the higher degree formula, Thesis,Northwestern Univ., Evanston, IL, USA, 2000.

27. B. Blander, Local projective model structures on simplicial presheaves, K-theory,v. 24(2001), no. 3, pp. 283-301; see also http : //www.math.uiuc.edu/K −

theory, no. 462.

28. B. Blander, A1-homotopy theory of schemes, Preprint, 2001, pp. 1-10, http ://www.math.uchicago.edu/ ∼ bblander

29. P. Hu, I. Kriz, Some remarks on real and algebraic cobordism, K-theory, 22(2001),no. 4, pp. 335-366; also http : //www.math.uiuc.edu/K − theory, no. 398.

30. Po Hu, I. Kriz, Steinberg relations in A1-stable homotopy theory, Intern. Math.Res. Notes, 2001, no. 17, pp. 907-912 (see also http : //www.math.uiuc.edu/K−

44

theory, no. 397).

31. P. Hu, Base change functors in the base changing homotopy category, Homology,Homotopy and applications, v.3, No. 2, (2001), pp. 417-454.

32. P. Hu, I. Kriz, Real-oriented homotopy theory and an analoque of the Adams-Novikov spectral sequence, Topology, 40(2001), no. 2, pp. 317-399.

33. D. Isaksen, Etale realization on the A1-homotopy theory of schemes, Adv.in Math., v. 184 (2004), no. 1, pp. 37-63; see also www.arXiv.org,math.KT/0106158, pp.1-22 (older version http : //www.math.uiuc.edu/K −

theory, no. 495, 2001, pp. 1-28.

34. Joshua R., Grothendieck-Verdier duality in enriched symmetric monoidal t-categories, Preprint, 2001, pp. 1-150, available at http : //www.math.ohio −

state.edu/ ∼ joshua.

35. D. Dugger, The Ω-spectrum for motivic cohomology, Preprint, 2001, pp. 1-14,available at http : //www.math.purdue.edu/ ∼ dugger

36. D. Dugger, The Zariski and Nisnevich descent theorems, Preprint, 2001, pp. 1-7,available at http : //www.math.uoregon/ ∼ dagger

37. J. F. Jardine, E2-model structure for presheaf categories, Preprint, 2001, pp.1-35, available at: http : //www.math.uwo.ca/ ∼ jardine

38. G. M. L. Powell, The adjunction between H(k) and DMeff (k), Preprint, 2001,pp. 1-22, available at http : //www.math.paris13.fr/ ∼ powell.

39. D. Dugger, D. Isaksen, Topological hypercovers and A1- realizations, Math. Zeit.,246(2004), pp. 667-689; see also http : //www.math.uiuc.edu/K − theory, no.528, 2001, pp. 1-21.

40. J. Riou, Theorie homotopique des S-schemas, Memoire DEA, see item I-20 above.

41. J. Riou, Fonctorialite des categories homotopiques, 2 exposes, pp. 1-8, 2001,http : //www.eleves.ens.fr : 8080/home/jriou/maths/dvi/fonctorialite.ps.gz

42. J. Riou, Structures monoidales sur SH(X), 2 exposes, Institut de Math. deJussieu, pp. 1-20, 2001, http : //www.math.jussieu.fr/ ∼ riou

43. J. Riou, Spectres de type fini, Preprint, 2002, pp. 1-17, http ://www.eleves.ens.fr : 8080/home/jriou/maths/dvi/type.finitude.ps.gz

44. B. I. Dundas, P. A. Ostvaer, O. Roendigs, Stable motivic homotopy theory,Preprint, 2001, pp.1-20, http : //www.math.utnu.no/ ∼ dundas/talk/Aahus.ps

45. B. I. Dundas, P. A. Ostvaer, O. Roendigs, Enriched functor and mo-tivic stable homotopy theory, Preprint, 2002, pp. 1-118, available athttp : //www.math.ntnu.no/ ∼ dundas/PP/motivic8.ps; see also http ://www.bieson.ub.uni − bielefeld.de/velltexte/2003/127/ps/teil2.ps.

46. O. Roendigs, Motivic functors: a well behaved model for stable motivic homotopy

45

theory, Preprint, 2000, pp. 1-13, available at http : //www.maths.gla.ac.uk/ ∼

ajb/ringspectra/roendings.ps.

47. O. Roendigs, Motivic functors, Dissertations, U. Bielefeld, Mai 2002, pp. 1-33,http : //archiv.ub.uni − bielefeld.de/disshabi/2002/0049/teil1.ps + teil2.ps

48. R. Joshua, Derived functors for maps of simplicial spaces, Journal of Pure andAppl. Algebra, v. 171 (2002), no. 2-3, pp. 219-248.

49. D. Dugger, S. Hollander, D. Isaksen, Hypercovers and simplicial presheaves,Math. Proc. Cambr. Phil. Soc., v. 136 (2003), no. 1, pp. 9-51; an olderversion available at http : //www.arXiv.org, E-print math.AT/0205027, pp.1-39,

50. J. F. Jardine, The separable transfer, Journ. of Pure and Appl. Algebra, v. 177(2003), no. 2, pp. 177-201, see also http : //www.math.uiuc.edu/K − theory,no. 449, 2000.

51. Po Hu, S-modules in the category of schemes, see item I-25 above.

52. S. Schwede, B. Shipley, Stable model categories are categories of mod-ules, Topology, v. 42 (2003), no. 1, pp. 103 - 153; see also http ://www.math.purdue.edu/ ∼ class.web.pdf .

54. F. Deglise, Modules homotopiques avec transfers et motifs generiques, These,Univ. Paris VII, Dec. 2002, pp. 1-337. available at http ://www.math.uiuc.edu/K − theory, no. 766, Jan. 2006.

55. F. Deglise, Modules de cycles et motives mixtes, Compt. Rend. Acad. Sci. Paris,t. 336 (2003), no. 1, pp. 41-46.

56. V. Voevodsky, Reduced power operations in motivic cohomology, see item II-6.38.

57. F. Loeser, Cobordisme des varietes algebriques (d’apres M. Levine et F. Morel),SeminaireN.Bourbaki, vol. 2001/02, expose 901, March 2002, pp. 1-28.

58. G. Powell, Steenrod operations in motivic cohomology, Preprint, 2002, pp. 1-90, available at http : //zeus.math.univ − paris13.fr/ ∼ powell/Postscript/2002/luminy.ps.gz.

59. F. Morel, Stable A1-homotopy theory I, Preprint, 2002, pp. 1-45, available athttp : //www.mathematik.uni − muenchen.de/ ∼ morel.

60. F. Morel, An introduction to A1-homotopy theory, see item I,20 above.

61. J. F. Jardine, Generalized sheaf cohomology theories, see item I-22 above.

62. V. Voevodsky, Open problems in the motivic stable homotopy theory I, see itemI-26 above.

63. V. Voevodsky, On the zero zero slice of the sphere spectrum, TrudyMat. Inst. Steklova, t. 246 (2004), Algebra-Geometric metody,svyazi i prilozh. (memory A. Tyurina), pp. 106-115 http :

46

//www.mathnet.ru/php/getFT.phtml?jrnid=tm&paperid=148&what... (Engl.transl: Proc. Steklov Inst. Math., 2004, No. 3, 93-102; see also http ://www.math.uiuc.edu/K − theory, no. 612, Dec. 2002, pp. 1-15.

64. B. I. Dundas, O. Roendigs, P. A. Ostvaer, Motivic stable homotopytheory, Preprint, 2003, available at http : //www.math.ntnu.no/ ∼

dundas/PP/DORII030805.ps

65. F. Morel, On the motivic πo of the sphere spectrum, in ”Axiomatic, enrichedand motivic homotopy theory, NATO Advanced Study Institute Series, Ser. II,v. 131, J. P. C. Greenlees (ed.), Elsever, 2003, pp. 219-260; see also http ://www.mathematik.uni − muenchen.de/ ∼ morel,

66. M. Levine, The homotopy coniveau filtration, Preprint, 2003, pp. 1-72, availableat the K-theory archive: http : //www.math.uiuc.edu/K − theory, no. 628.

67. J. Hornbostel, Chromatic motivic homotopy theory, Preprint, no. 642, June 2003,pp. 1-77, available at the K-theory archive http : //www.math.uiuc.edu/K −

theory, no. 642.

68. M. Spitzweck, Operads, algebras and modules in model Categories and mo-tives, PhD Thesis, Gottingen, 2003, pp. 1-77, available at http : //www.uni −math.gwdg.de/spitz/diss.ps for its homotopy-theoretical part see also E-printhttp : //www.arxiv.org, math.AT/0101102, 2001, pp. 1-48.

69. D. Dugger, J. Isaksen, Motivic cell structures, Algebraic and Geometric Topology,v. 5(2005), pp. 615-652, see also an older version at the K-theory archive,http : //www.uiuc.edu/K − theory, no. 660, pp. 1-27.

70. S. Borghesi, Algebraic Morava K-theories, Invent. Math., v. 151(2003), no. 2,pp. 381-413, see also http : //www − math.math.univ − paris13.fr/prepub/pp2001 − 17.ps.gz, pp. 1-48.

71. B. Dundas, O. Roendigs, P. A. Ostvaer, Motivic functors, Documenta Math.,8(2003), pp. 489-525.

72. J. F. Jardine, Categorical homotopy theory, Homology, Homotopy and applica-tions, Homology Theory, Homotopy theory and Applications, v. 8 (2006), no. 1,pp. 71-144; see also http : //www.math.uiuc.edu/K− theory, no. 669, 2005, pp.1-79.

73. F. Morel, On cohomology operations in unramified Milnor K-theory, Preprint,Oct. 2003, pp. 1-22, available at http : //www.mathematik.uni −

muenchen.de/ ∼ morel

74. F. Morel, Serre’s splitting principle and the motivic Barrat-Priddy-Quillen theo-rem, Preprint, Oct. 2003, pp. 1-8, available at http : //www.mathematik.uni −muenchen.de/ ∼ morel

75. F. Morel, Milnor’s conjecture on quadratic forms and mod 2 motivic com-plexes, Rendiconti del Seminairio Matematico della Universita di Padova, t.

47

114 (2005), pp. 63-111; see also Preprint, Dec. 2004 available at http ://www.mathematik.uni − muenchen.de/ ∼ morel

76. F. Morel, Milnor’s conjecture on quadratic forms and the operation Sq2,Preprint, Dec. 2003, pp. 1-11, available at http : //www.mathematik.uni −muenchen.de/ ∼ morel.

77. F. Morel, The stable A1-connectivity theorems, K-theory, 2004, pp. 1-57 (toappear); see also http : //www.mathematik.uni − muenchen.de/ ∼ morel, pp.1-73.

78. J. Ayoub, La theorie locale des cycles evanescent dans les categories motiviques,Preprint, 2004, pp. 1-34, available at http : //www.math.jussieu.fr/ ∼ ayoub.

79. D. Isaksen, Flasque model structure for presheaves, Preprint, Jan. 13, 2004, pp.1-17, available at http : //www.arXiv.org, no. math.AT/0401132.

80. W. Dwyer, Localizations, in ”Axiomatic, enriched and motivic homotopytheory, NATO Advanced Study Institute Series, ser. II, v. 131, J. P.C. Greenlees (ed.), Elsevier Sci. Publ., 2003, pp. 3-28; see also http ://hopf.math.purdue.edu/Dwyer/local.ps.gz

81. J. Horbostel, S. Yagunov, Rigidity for henselian local rings and A1-representabletheories, Preprint, 2004, pp. 1 - 13, available at the K-theory archive, http ://www.math.uiuc.edu/K − theory, no. 688.

82. M. Levine, The Postnikov tower in motivic stable homotopy theory, Preprint, pp.1-16, available at the K-theory archive, http : //www.math.uiuc.edu/K−theory,no. 692, May, 2004.

83. F. Morel, On the A1-homotopy and A1-homology sheaves of algebraic spheres,Notices of a course at Inst. Henri Poincare, Paris, given in May, 2004; ver-sion of April 2007, pp. 1-50, available at http : //www.mathematik.uni −muenchen.de/ ∼ morel.

84. J. F. Jardine, Motivic spaces and motivic stable category, lectures at the Amer-ican Institute of Math. Workshop ”Motives, homotopy theory of varietiesand dessins d’enfants”, Palo Alto, CA, April, 2004, pp. 1-22, available athttp : //www.aimath.org/WWN/motivesdessins/motivic/pdf .

85. O. Roendigs, Functoriality in motivic homotopy theory, Preprint, 2006, pp. 1-60, available at http : //www.mathematik.uni − bielefeld.de/ ∼ oroendig/functoriality.dvi.

86. O. Roendigs, P.- A. Ostvaer, Modules over motivic cohomology, Advancesin Math., v. 219(2008), no. 2, pp. 689-727; see also http : //www.mathematik.uni − bielefeld.de/ ∼ oroendig/MZfinal.pdf

87. B. Guillou, Unstable A1-homotopy theory, Expose, Univ. of Chicago, 2004, pp.1-6, available at http : //www.math.uchicago.edu/ ∼ bertg/A1htpy.pdf , or http :

48

//www.math.illinois.edu/ ∼ bertg/A1htpy.pdf ; http : //www.uiuc.edu/ ∼

bertg/A1htpy.pdf .

88. B. Guillou, Stable A1-homotopy theory, Expose, Univ. of Chicago, 2004, pp.1-5, available at http : //www.math.uchicago.edu/ ∼ bert/StableA1htpy.pdf , orhttp : //www.math.uiuc.edu/ ∼ bertg/StableA1htpy.pdf .

89. D. Dugger, D. Isaksen, Weak equivalences of simplicial presheaves, in ”Homo-topy Theory, relations with Algebraic Geometry and Group Cohomology andAlgebraic K-theory”, Evanston, IL, 2003, Contemp. Math., v. 346(2004), AMS,Providence, pp. 97-114.

90. R. Jardine, Higher order automata, cubical sets and some conjec-tures of Grothendieck, Preprint, 2004, pp. 1-25, available at http ://www.math.uwo.ca/ ∼ jardine/ATMCS2/Jardine.pdf

91. S. Borghesi, Algebraic Morava K-theory spectra over perfect fields, Prepubbli-cazione, http : //www.sns.it , 2003.

92. S. Borghesi, Extension of (co)homological theories, Geometry Seminars, 2001-2004, pp. 1-15, Univ. Stud. Bologna, Bologna, 2004.

93. S. Borghesi, Degrees formulas, Boll. Unione Mat. Ital. Sez. B, Artic Ric. Mat.,8 (2005), no. 1, pp. 133-144; see also http : //www.sns.it/Geometria, (2003).

94. J. Ayoub, Formalisme des 4 operations, Institut de Math. de Jussieu, 2004, pp.1-165, available at http : //www.math.uiuc.edu/K − theory, no. 717; see alsohttp : //www.math.jussieu.fr/ ∼ ayoub, pp. 1-163.

95. J. Ayoub, Applications diverses des operations et du theoreme de change-ment de base pour morphisme projective, Preprint, available at http ://www.math.jussieu.fr/ ∼ ayoub, Avril, 2005, pp. 1-53.

96. J. Ayoub, The motivic vanishing cycles and the conservation conjecture, in ”Al-gebraic Cycles and Motives”, vol. 1, London Math. Soc. Lect. Notes Ser. vol.343 (2007), pp. 3-54, see item I-45 above; see also http : //user.math.uzh/ayoub,pp. 1-42.

97. O. Roendigs, P. A. Ostvaer, Modules over motivic cohomology, Advances inMath., 219, no. 2 (2008), pp. 689-727, see also http : //www.mathematik.uni−bielefeld.de/ ∼ oroending/MZfinal.pdf

98. F. Deglise, Transferts sur le groupes de Chow a coefficients, Math. Zeit., b.252(2006), no. 2, pp. 315-343.

99. Roendigs, P. A. Ostvaer, Motivic spaces with transfers, Preprint, 2006.

100. C. Casacuberta, Homotopy localization with respect to proper classes of maps,in Proc. of the Conf. on Groups Homotopy and Configuration Spaces, Tokyo,2005, pp. 1-12 (to appear), available at http : //www.faculty.ms.tokyo.ac.jp/ ∼ topology/GHC/data/Casacuberta.pdf .

49

101. G. Quick, Profinite etale cobordisms, Thesis, Univ. Muenster, 2005, pp. 1-115, available at http : //www.math1.uni−muenster.de/inst/deninger/about/pubikat/quick/01.ps or http : //miami.uni − muenster.de/servlets/DerivateServlet...

102. J. Riou, Dualite de Spanier-Whitehead en geometrie algebrique, Comptes RendusAcad, Sci., Paris, Ser. I, t. 340 (2005), pp. 431-436.

103. M. G. Decker, Loop spaces in Motivic homotopy theory, Thesis, Texas A&Muniversity,Aug. 2006, available at http : //txspace.tamu.edu/bitstream/1969.1/EDT −

1808/DECKER − DISSERTATION.pdf

104. N. Yagita, Applications of Atyiah-Hirzebruch spectral sequence for motivic cobor-dism, Proceedings of the London Mathematical society, v. 90 (2005), no. 3, pp.783-816; see also http : //www.math.uiuc.edu/K − theory, no. 627, pp. 1-30.

105. M. Levine, Motivic tubular neighborhoods, Documenta Mathematica 13(2007),71-146, see also http : //www.arXiv.org, no. math/AG 0509463, pp. 1-55.

106. F. Morel, A1-homotopy classification of vector bundles over smooth affineschemes, Preprint, available at http : //www.mathematik.uni−muenchen.de/ ∼

morel/bgln.pdf , 20 Nov. 2007, pp. 1-72.

107. J. Ayoub, Motivic version of the classical polilogarithms, in Arbeitsgemanschaftmit aktuallen Thema: Polylogarithms, Mathematisches Forschungsinstitut Ober-wolfach, Oct. 9th. 2004, Report no. 48/2004, pp. 1-5?

108. J. Ayoub, Les six operations de Grothendieck et le formalisme des cyclesevanessant dans le monde motivique, Asterisque, no. 314 (2008), 464pp,http : //www.math.univ − paris13.fr/%7Eayoub, 583pp; the original version:These, Institut de Mathematiques de Jussieu, pp. 1-418, 2005, available athttp : //www.math.uiuc.edu/K − theory, no. 761, Dec. 2005.

109. Algebraic cobordism, Arbeitsgemeinschaft mit aktuellen Thema, Organizedby M. Levine and F. Morel, Mathematisches Forschungsinstitut Oberwol-fach, April, 2005, Report no. 16/2005, pp. 1-44, available at http ://www.mfo.de/programme/ schedule/2005/14/OWR 2005 16.ps..

110. J. Ayoub, The motivic Thom spectrum MGL and the algebraic cobordism Ω∗(−),in ”Algebraic Cobordism”, see item [VIII-108] above.

111. F. Morel, Structure of A1-homotopy sheaves I, Preprint, pp. 1-81; available atthe K-theory archive, http : //www.math.uiuc.edu/K − theory, no. 794, July,2006.

112. F. Morel, A1-Algebraic topology over a field, Preprint, Nov. 2006, pp. 1-148;available at the K-theory archive http : //www.math.uiuc.edu/K − theory, no.806; see also http : //www.math.lmu.de/ ∼ morel .

113. J. Hornbostel, Localizations in motivic homotopy theory, Math. Proc. of the

50

Cambridge Phil. Soc., v. 140(2006), No. 1, pp. 95-114.

114. O. Roendigs, P. Ostvaer, Motives et Modules sur la Cohomologies motiviques,Comptes Rendus Acad. Sci., Paris, t. 342 (2006), no. 10, pp. 751-754.

115. R. Jardine, Diagrams and torsors, K-theory, 37(2006), pp. 1-20; see also http ://www.math.uiuc.edu/K − theory, no. 723.

116. M. Levine, Chow moving lemma and homotopy coniveau tower, K-theory, v.37 (2006), no. 1-2, pp. 1-68??, an early version http : //www.arxiv.org,math.AG/0510201v1, Oct. 10, 2005, pp. 1-78

117. G. Quick, Stable etale realizations and etale cobordism, Advances in Math.,v. 214 (2007), pp. 730-760; see also http : //www.arxiv.org, no.math.AG/0608313, Aug. 2006, pp. 1-31.

118. F. Morel, Rationalized motivic sphere spectrum and rational motivic cohomol-ogy, Preprint, 2006, pp. 1-9; available at http : //www.mathematik.uni −muenchen.de/ ∼ morel

119. S. Schwede, Shipley B., Classification of stable modul categories, Classificationof stable model categories, Preprint, 200??, pp. 1-43.

120. O. Roendigs, Functoriality in motivic homotopy theory, Preprint, 2006,pp. 1-60, available at http : //www.mathematik.uni − bielefeld.de/ ∼

oroendig/functoriality.dvi.

121. M. Severitt, Motivic homotopy types of projective curves, Univ. Beilefeld, Diplo-marbeit, 2006, Preprint, pp. 1-99, available at http : //www.mathematik.uni −bielefeld.com/ ∼ mseverit/mseverittse.pdf or www.math.uni−bielefeld.de/ ∼

rost/data mseveritt.ps

122. N. Rozenblum, Motivic homotopy theory and power operations in motivic coho-mology, MA Thesis, Harvard Univ., 2006, pp. 1-40, http : //math.mit.edu/ ∼

nrozen/papers/motivic.pdf .

123. A. Asok, B. Doran, On unipotent quotients and some A1- contractable smoothschemes, Internat. Math. Research Papers, (2007), no. 5, pp. 1-51; seealso http : //imrp.oxfordjournals.org/cgi/reprint/2007/rpm005/rpm005.pdf ;an older version available at arxiv : math/0703137v2 , [math.AG], pp. 1-40.

124. B. I. Dundas, Prerequisites in Algebrtaic Topology, in: ”Motivic Homotopy The-ory”, Lectures at the Summer School at Nordfjordeid, 2002, Berlin, Springer,2007 (see item I.46 above), pp. 1-60; see also http : //www.math.ntnu.no/ ∼

dundas.

125. V. Voevodsky, Lectures on motivic stable homotopy theory, in: ”MotivicHomotopy Theory”, Lectures at a Summer School at Nordfjordeid, 2002,Berlin Springer, 2007, pp. 147-221 (see item I.43 above), see also http ://www.uwo.edu/ ∼ oroendigs.

51

126. J. Riou, Categorie homotopique stable d’un site suspendu avec intervalle,Bull. Soc. Math. France, t. 135(2007?), pp. 495-547. see also http ://www.math.uiuc.edu/K − theory, no. 825, 2007, pp. 1-52; or http ://www.math.jussieu.fr/ ∼ riou,

127. F. Morel, Rational stable splitting of Grassmannian and rational mo-tivic sphere spectrum, Preprint, pp. 1-13, 2007??, available at http ://www.mathematik.uni − munchen.de/ ∼ morel

128. I. Panin, K. Pimenov, O. Rondigs, On Voevodsky’s algebraic K- theory spectrum,in: Algebraic Topology: The Abel Symposium 4, eds: N. Baas, E. Friedlander, P.-A. Ostvaer, pp. 279-330, Springer, 2009; see also arXiv:0709.3905v1, [math.AG];an older version at http : //www.math.uiuc.edu/K − theory, no. 8??.

129. I. Panin, K. Pimenov, O. Roendigs, A universality theorem for Voevodsky’s al-gebraic cobordism spectrum, Homology, Homotopy and their Applications, v. 10(2008), no. 2, pp. 211-228; see also arXiv : 07094116v1, [math.AG]; an olderversion at http : //www.math.uiuc.edu/K − theory, no. 846.

130. B. Guillou, A short note on models for equivariant homotopy theory, Preprint,2007, pp. 1-9, http : //www.math.uchicago.edu/ ∼ bert/EquiModels.pdf .

131. M. Wendt, On fibre sequences in motivic homotopy theory, Ph. D. Disserta-tion, Univ. Leiptsig, June, 2007, pp. v+ 1-175, available at http : //www.mathematik.uni − leipzig.de/ ∼ huber, or http : //home.mathematik.uni −freiburg.de/arithmetische − geometrie/preprints/wendt − diss.pdfor http : //www.mathematik.uni−regensburg.de/preprints/Preprints2007/10−2007.pdf .

132. A. Asok, D. Doran, A1-homotopy groups and smooth toric varieties, Preprint,Aug., 2007. pp. 1-42, http : //www.math.washington.edu/ ∼ asok/toricA1.pdf .

133. A. Asok, A1-homotopy types and contractible smooth surfaces, Preprint,Aug. 2007, pp. 1-23, available at http : //www.math.washington.edu/∼ asok/papers/exoticllb − contractibleF inal.pdf .

134. F. Neumann, J. Rodriguez, The cellularization of simplicial presheaves and mo-tivic homotopy, Topology and its applications, 154 (2007), no. 7, pp. 1481-1488;also available at http : //www.math.le.ac.uk/people/frneumann/celles.pdf

135. O. Roendigs, P. A. Ostvaer, Rigidity in motivic homotopy theory, Math. Ann.,341 (2008), no. 3, pp. 651-675, see also http : //www.math.uio.no/ ∼

paularne/rigidityma.pdf

136. A. Asok, B. Doran, A1-homotopy types, excision and solvable quotients, Ad-vances in Math., v. 221 (2009), no. 4, pp. 1244-1190; see also http ://www.arXiv.org, no.0902:156, [math.AG], 10 Feb. 2009, pp. 1-48.

137. M. Levine, Homotopy coniveau tower, Journal of Topology, 1(2008), pp. 217-267,http : //jtopol.oxfordjournals.org/cgi/reprint/1/1/217.pdf .

52

138. A. Asok, B. Doran, Homotopy theory of smooth affine quadrics re-visited, Preprint, Mar. 2008, pp. 1-24, available at http ://www.math.washington.edu/ ∼ asok/papers/QuadricsRev1.pdf .

139. A. Holmstrom , Questions and speculations on cohomology theories in arith-metic geometry, Preprint, 2007, pp. 1-29, available at http : //www.andreasholmstrong.org/research/Cohomology1.pdf .

140. S. Zoghaib, Theorie homotopique de Morel-Voevodsky et applications, MemoireDEA, Univ. Paris VI, 2006/2007, 45pp., available at http : //www.mmfai.ens.fr/memoires/2007/zoghaib.pdf , or http : //www.normalsup.org/ ∼

zoghaib/math/dea.pdf .

141. S. Zoghaib, Autour de la thieorie homotopique de Morel-Voevodsky, Preprint, pp.1-8, 200?, available at http : //www.fimfa.ens.fr/memoires/2007/zoghaib.

142. G. Quick, Profinite homotopy theory, Documenta Math., v. 13 (2008), pp. 585-612; see also http : //www.arXiv.org, no. 0803.4082, Mar. 28, 2008.

143. S. Hakon, S. Bergsaker, Homotopy theory of preseaves of Gamma- spaces, E-print, May 12. 2008, pp. 1-33, availble at http : //www.arXiv.org, no.0805.1529v1, [math.AT].

144. M. Spitzweck, Slices of motivic Landweber spectra, E-print, May 2008, 11pp.,arXiv : 0905, 3350v1, [math.AT].

145. N. Naumann, M. Spitzweck, P.-A. Ostvaer, Motivic Landweber exactness, E-print, pp. 1-40, 2 June, 2008, available at arXiv : 0806.0274v1, [math.AG].

146. M. Spitzweck, Relations between slices and quotients of the algebraic cobor-dism spectrum, E-print, 3 Dec., 2008, pp. 1-13; available at arXiv:0812.0749v1,[math.AG].

147. M. Levine, Smooth motives, in: Motives and algebraic cycles: a celebration inhonor of Spencer J. Bloch, Fields Institute Communications, v. 56 (2009), pp.175-232; see also http : //www.arXiv.org, no. 0807.2265v1 [math.AG], June,2008, pp. 1-65.

148. M. Levine, Oriented cohomology, Borel-Moore homology and algebraic cobor-dism, Mich. Math. J., 57 (2008), pp. 523-527; see also http : //www.arXiv.org,0807.2257v1, [math.KT], pp. 1-47.

149. M. Levine, Comparison of cobordism theories, Journ. of Algebra, v. 322 (2009),no. 9, pp. 3291-3317; see also http : //www.arXiv.org, 0807.2238v1, [math.AG].

150. Po Hu, I. Kriz, K. Ormsby, Remarks on motivic homotopy theory over alge-braically closed fields, Jour. of K-theory, v. 7(2011), no. 1, pp. 55-89; see alsohttp : //www.math.uiu.edu/K − theory, no. 903?, Aug. 2008, pp. 1-19.

151. J. Ayoub, Note sur les operations de Grothendieck et la realization deBetti, E-print, available at: http : //user.math.uzh.ch/ayoub/PDF − Files/

53

Realization − Betti.pdf pp. 1-25; older version: http : //www.math.uiuc.edu/K − theory, no. 910 (2008), pp. 1-20.

152. A. Asok, F. Morel, Smooth varieties up to A1-homotopy and algebraic h-cobordisms, Advances in Math., v. 277(2011), no. 5; 1990-2058; see alsohttp : //www.math.lsu.de/ ∼ morel/hcobordisms.pdf , pp. 1-62??; an olderversion: http : //arXiv.org, no. 0810.0324v5, [math.AG], Apr.. 14, 2011, pp.1-71.

153. A. Asok, B Doran, A1-homotopy types and contractible smooth schemes, DukeMath. Journ. (to appear, 2008), see also http : //www.math.washington.edu/ ∼ asok/papers/exoticllb − contractible.pdf .

154. U. Choudhury, Homotopy theory of schemes and A1-fundamental group,Dissertation, U. Padova, June, 2008, pp. 1-70, available at http ://www.math.u−bordeaux.fr/ALGANT/documents/theses/choudhury.pdf , orhttp : //www.algant.eu/documents/theses/choudhury.pdf

155. K. M. Ormsby, Some remarks on 2-completed motivic homotopy theory and themotivic J-homomorphism, AMS special session on homotopy theory and highercategories, Jan. 2009, pp. 1-22, available at http : //www.math.uchicago.edu/ ∼

fiore/OrmsbySlides.pdf , or http : //www.math.mit.edu/ ∼ orsby/2 −

completeStableHtpy.pdf

156. D. Dugger, D. Isaksen, The motivic Adams spectral sequence, Geometry andTopology, 14(2010), no.2, pp. 967-1014; ealier version: http : //www.arXiv.org,no. 0901.1632, [math.AG], pp. 1-35, 13 Jan. 2009.

157. D. Isaksen, The cohomology of the motivic A(2), Homology, Homotopy and Ap-plications, 11(2009), 251-274; see also arXiv:0903.5217v1, [math.AT], July 2009,pp. 1-24.

158. M. Hill, Ext and the motivic Steenrod algebra over R, Journ, of Pure Appl.Algebra, v. 215 (2011), no. 5, 715-727; see also arXiv:0904.1998v1, [math.AT],pp. 1-14, 14 Apr. 2009.

159. S. Gorchinsky, Guletsky V., Symmetric powers in stable homotopy categories,E-print, pp. 1-59, available at arXiv:0907.0730, [math.AG]i, July 3, 2009.

160. M. Spitzweck, Periodizable motivic ring spectra, E-print, July 9, 2009, pp, 1-15,available at arXiv:0907.1510v1, [math.AG].

161. Wendt M., On homotopy limits amd colimits of simplicial sheaves, Preprint,Jan.? 2009, pp. 1-24, available at http : //home.math.uni − freiburg.de/arithmetische − geometrie/peprints/wendt − hocolim.pdf .

162. F. Morel, Serre classes in A1-homotopy theory and the Friedlander-Milnor con-jecture, Jan. 2009, pp. 1-9, available at http : //www.math.lmu.de/ ∼ morel.

163. F. Morel, The Friedlander-Milnor conjecture, Preprint, 2009, pp. 1-37 (verypreliminary), available at http : //www.math.lmu.de/ ∼ morel.

54

164. J. F. Jardine, Representability theorem for simplicial presheaves, Preprint, June,2009, pp. 1-25, available at http : //www.math.uwo.edu/simjardine/papers/.

165. A. Roig-Maranges, Descent for blow-up’s on smooth schemes, Preprint, pp. 1-16, 15 April, 2009, available at http : //ma1.upc.edu/recerca/preprints/2009//prepr200901/roigmarange.pdf .

166. N. Naumann, M. Spitizweck, Brown representability in A1-homotopy theory, E-print, Sept. 2009, pp. 1-10, http : //www.arXiv.org: 0909.1943v1.

167. D.-C. Cisinski, Algebre homotopique et cohomologie, l’Habilitation a Diriger desRecherches, Memoire de synthese, pp. 1-35, Dec. 2008, Univ. Paris 13, availableat http : //www.math.univ − paris13.fr/ ∼ cisinski/

168. B. Kahn, On the classifying space of a linear algebraic groups, a talk at theWorkshop on motivic homotopy, Munster, July 30, 2009, pp. 1-39, available athttp : //people.math.jussieu.fr/ ∼ kahn/preprints/BG − Munster.pdf

169. P. Herrmann, F. Strunk, A note on implicial functors and motivic homotopytheory, Preprint, 2009, pp. 1-17, http : //www.math.uni − bielefeld.de/ ∼

pherrman/files/simplfunc.pdf ; or http : //www.mathematik.uni −

osnabruek/staff/phpapers/pherrmann/simplfunc.pdf , or http : //d −

mathnet.preprint.org/staff/staff/phpages/pherrmann

170. P. Herrmann, A model for motivic homotopy theory, June, 2009, pp. 1-49,http : //www.math.uni−bielefeld.de/pherrman/kolleg−seminar−090609.pdf

171. Ch. Cazahave, Algebraic homotopy classes of rational functions E-print, pp.1-26, availabe at arXiv:0912.2227v1, [math.AT], 11 Dec. 2009.

172. Cazanave, Theorie homotopique des schemas d’Atiyah et Hitchin, Doc-toral thesis, U. Paris-13, Mar. 2009, pp. 1-167, available at http ://math.unice.fr/ ∼ cazanave/Documents/these.pdf , or http : //tel.archives−ouvertes.fr/dosc/00/46/36/80/PDF/thesieCazanave.pdf

173. P. Pelaez, Motives and slice filtration, Motives and slice filtration, Comptes ren-dus Acad. Sci. Paris, t. 347 (2009), nn. 9-10, pp. 541-544. vskip 2mm

174. P. Pelaez, On the functoriality of the slice filtration, E-print, pp. 1-12,arXiv:1002.0317v1, [math.KT], 1 Feb. 2010.

175. Hu P., Kriz I., Ormsby K., Equivariant and real stable homotopy theory,Preprint, 13 Feb. 2010, pp. 1-42, availabe at the K-theory archive http ://www.math.uiuc.edu/K − theory, no. 952.

176. Po Hu, I. Kriz, K. Ormsby, Convergence of the motivic Adams spectral sequence,E-print, pp. 1-19, 6 May, 2010, availabe at http : //www.math.uiuc.edu/K −

theory.

177. K. Ormsby, Computation in the stable motivic homotopy theory, Dissertation,Univ. of Michigan, pp. 1-90, 2010, http : //deepblue.lib.umich.edu/bitstream/2027.42/77824/ormsby 1.pdf .

55

178. M. Levine, Slices and transfers, Documenta math., Extra vol.: Andrei A. Suslin’ssixtieth birthday (2010), pp. 393-443; see also arXiv:1003.1830, [math.AG],March, 2010.

179. J. Hornbostel, Preorientations of the derived motivic multiplicative group, E-print, 25 May, 2010, pp. 1-48, available at arXiv:1005.4546v1.

180. M. Wendt, Classifying spaces and fibrations of simplicial sheaves, E-print, pp.1-34, arXiv:1009.2930v1, [math.AT], 15 Sept. 2010.

181. I. Panin, C. Walter, Quaternionic Grassmannians and Pontryagin classes, in al-gebraic geometry, E-print, pp. 1-43, arXive:1011.0649, [math.AG], 2 Nov. 2010;or K-theory archive http : //www.math.uiuc.edu/K − theory, no. 977, 2 Nov.,2010; or http : //math.uni − bielefeld.de/LAG/man/405.dvi, Sep 10, 2010.

182. I. Panin, C. Walters, On the motivic commutative ring spectrum BO,E-print, pp. 1-39, arXive:1011:0650, [math.AG], 2 Nov., 2010; or K-theory archive, no. 978, 2 Nov. 2010, also http : //www.math.uni −

bielefeld.de/LAG/man/406.dvi.

183. I. Panin, C. Walters, On the algebraic cobordism spectra MSL and MSp, E-print, pp. 1-32, arXive: 1011.0652, [math.AG], 2 Nov. 2010; or K-theoryarchive, no. 979, 2 Nov. 2010.

184. I. Panin, C. Walter, On the relation of symplectic algebraic cobordism to Her-mitian K-theory, E-print, pp. 1-12, arXive:1011.0653, [math.AG], 2 Nov. 2010,or K-theory archive, no. 980, 2 Nov. 2010.

185. B. Drew, Descente: Nisnevich et cdh, in: Descente cohomologique, localizationet constructubilite dans les categories motiviques, Groupe de travaile a l’Univ.Paris 13, 2010, Printemps 2010, expose VII, pp. 1-11, http : //www.math.univ−paris13.fr.

186. S. Haehne, Semistable symmetrische spectren in der A1-homotopietheorie, Diplo-marbeit, pp. 1-81, Universitaet Bonn, Juni, 2010, http : //www2.math.uni −wuppertal.de/hornbost/haehne.pdf .

187. A. Asok, Biratonal invariants and A1-connectedness, E-print, 26 Jan. 2010, pp.1-38; available at arXiv:1001.4574v1, [math.AG].

188. M. Wendt, On the A1-fundamental groups of smooth toric varieties, Advaces inMath., 223, no. 1 (2010), pp. 352-378; see also http : //www.mathematik.uni−regensburg.de/preprints/Forschergruppe/Preprints2007/09 − 2007.pdf , orhttp : //home.mathematik.uni − freiburg.de/arithmetische − geometrie/preprints/wendt − toric.pdf/

189. M. Wendt, Fibre sequence and localization of simplicial sheaves, E-print, pp.1-26, arXiv:1011.4784v1, [math.AT], 22 Nov. 2010.

190. J. F. Jardine, Representability in model categories, J. Pure and appl. algebra,215(2011), pp. 77-88; see also http : //www.math.uwo.ca/ ∼ jardine/papers

56

/preprints/rep3a.pdf , 2010, pp. 1-15.

191. M. Wendt, More examples of motivic cell structures, E-print, pp. 1-10,arXiv:1012.0454v1, [math.AT], 2 Dec. 2010.

192. M. Spitzweck, Another viewpoint on J-spaces, E-print, pp. 1-7, 6 Dec. 2010,arXiv:1012.1264, [math.AG].

193. J. Gutiierrez, O. Roendigs, M. Spitzweck, P. A. Ostvaer, Motivic slices and col-ored operads, J. of Topology, v?? (2012), pp. 1- 29??; or E-print, pp. 1-35, 15Dec. 2010, arXiv:1012.3301v1, [math.AG].

194. M. Levine, Slice filtration and Grothendieck-Witt groups, E-print, 30 Dec. 2010,pp. 1-41, arXiv:1012.5630v1, [math.AG].

195. A. Asok, Ch. Haesemeyer, Stable A1-homotopy and R-equivalence, Journ. ofpure and appl. algebra, v. 215 (2011), no. 10, pp. 2469-2472; see also E-print,arXiv:1011.3186, [math.AG], 14 Nov. 2010, pp. 1-5.

196. A. Asok, A1-contractability and topological contractability, Lectures in Ottawa(2lect), pp. 1-14, 2011, www.bcf.usc.edu/ ∼ asok/notes/OttawaLectures.pdf .

197. S. Gorchinsky, V. Guletskii, Positive model structures for abstract symmetricspectra, E-print, arXive:1108.3509, [math.AT], pp. 1-22??, Aug. 17, 2011.

198. G. Carlsson, R. Joshua, Motivic Spanier-Whitehead diality and themotivic Becker-Gottlieb transfer, Preprint, pp. 1-31, 2011, http ://www.math.osu.edu/ ∼ joshua/Mot − Sd10.pdf

199. G. Carlsson, R. Joshua, Equivariant motivic homotopy theory, Preprint, 2011,pp, 1-31, http : //www.math.osu.edu/ ∼ joshua/EquivMottheory.pdf .

200. G. Carlsson, R. Joshua, Galois equivariant motivic homotopy theory, Preprint,2011, pp. ???

201. P. Arndt, Homotopy-theoretic models of type theory, in: Typed lambda calculiand applications, Springer, 2011, 10th international conference, eds. ????

202. P. Arndt, C. Kapulkin, Homotopy theoretical models of type theory, Lec-ture Notes in Computer sci. 6990, pp. 45-60 (2011), a corrected version:arXiv:1208.5683v2, [math.LO], [math.AT], pp. 1-15, Wed., 12 Aug. 2012.

203. S. Yagunov, Remark on rigidity over several fields, Homology, Homotopy and ap-plications, v. 13 (2011), pp. 159-164; see also http : //www.math.uiuc.edu/K −

theory, no. 1015, Nov. 6, 2011.

204. M. Hadian, Motivic fundamental groups and integral points, Duke M. J., v.160(2011), no. 3,

205. F. Deglise, Orientation theory in arithmetic geometry, E-print, pp. 1-23,arXiv:1111.4203v1, [math.AG], 17 Nov., 2011.

57

206. P. Pelaez, Birational motivic homotopy theories and the slice filtration, E-print,pp. 1-18, arXiv:1112.2358v1, [math.KT], 11 Dec. 2011.

207. P. Pelaez, On the orientablity of the slice filtration, Homology, Homotopy andappl., v. 13 (2011), no. 2, pp. 293-300; see also arXiv:1009.1055v1, [math.AG],21 Sept. 2010, pp. 1-9.

208. M. Hoyois, On the relation between algebraic cobordism and motivic coho-mology, Preprint, pp. 1-19, Dec. 2011, http : //math.northeastern.edu/ ∼

hoyois/papers.

209. M. Hoyois, The motivic cohomology of some quotients of MGL, Preprint, pp.1-13, Dec. 2011, http : //math.northwestern.edu/ ∼ hoyois/papers/.

210. M. Levine, A comparison of motivic and classical stable homotopy theories, E-print, arXiv : 1201 : 0283v1, [math.AG], Dec. 31, 2011, pp. 1-32; or K-theoryarchive, http : //www.math.uiuc.edu/K − theory, no. 1022, Jan 1, 2012, pp.1-32.

211. M. Levine, Convergence of the Voevodsky’s slice tower, E-print, arXiv :1201.0279v1, [math.AG], Dec. 31, 2011, pp. 1-20?, or K-theory archive,http : //www.math.uiuc.edu/K − theory, no. 1021, Jan. 1, 2012, pp. 1-20.

212. P. Pelaez, The unstable slice filtration, E-print, pp. 1-21, arXiv:1201.3657v1,[math.KT], 17 Jan. 2012.

213. F. Morel, On the Friedlander-Milnor conjecture for groups of small ranks,Preprint, 2011, pp. 1-64, http : //www.mathematik.uni − muenchen.de/ ∼

morel/Harvard.pdf .

214. A. Krishna, The motivic cobordism for group actions, E-print,arXiv:1206.5952v1, [math.AG], pp. 1-68, June 26, 2012.

215. A. Ananyevskiy, The special linear version of projective bundle theorem, E-print,arXiv:1205.6067v1, [math.AG], May 28, 2012, pp. 1-33; or http : //math.uni −bielefeld.de/LAG/man/471.dvi.

216. M. Hoyois, Motivic Steenrod algebra over perfect fields, Preprint, 2012, pp.1-??, available at: http : //math.northwestern.edu/ ∼ hoyois/papers/motivicsteenrod.pdf

217. J. Riou, Operations de Steenrod motiviques, E-print, arXiv:1207.3121v1,[math.AG], 12 July, 2012, pp. 1-61.

218. J. Gutierrez, O. Rondigs, M. Spitzweck, P. A. Ostvaer, Motivic slices andcolored operads, J. of Topology (2012), pp. 1-29 (to appear);, see alsoarXiv:1012.3301v2, 13 Apr., 2012.

219. U. Choudhury, On a conjecture of Morel, E-print, 2012, pp. 1-12,arxiv:1209.0484v1, [math.AG], [math.KT], 3 Sept. 2012.

220. Ch. Cisinski, Habilitation, Univ. Paris. 13, 2012?, http : //www.math.univ −

58

tousouse.fr/ ∼ cisinsk/hab.pdf ,

221. Nguyen Le Dang Thi, Stable A1-connectedness, E-print, pp. 1-5,arXiv:1208.5415v2, [math.KT], 3 Sept., 2012, 6Kb.

222. K. Ormsby, P. A. Ostvaer, Motivic Brown-Peterson invariants of rationals, E-print, pp. 1-30, arXiv:1208.5007v1, Aug. 2012.

223. M. Hoyois, From algebraic cobordism to motivic cohomology, J. f. d. Reine Ang.Math. (to appear), arXiv:1210.7182v4, [math.AG], 29 Apr. 2013, pp. 1-???

224. D. White, On colimits in various categories of manifolds, Preprint, 17Dec. 2012, pp. 1-8; http : //dwhite03.web.wesleyan.edu/files/Expository/OnColimitsofvariouscategoriesofmanifolds.pdf .

225. T. Gregersen, A singular?? construction of motivic homotopy theory, folk.uio.no

226. A. Krishna, Jingyin Park, Semi-topologization in motivic homotopy theory andapplications, E-print, arxiv:1302.2218, Feb. 9, 2013, pp. 1-???.

227. F. Muro, O. Raventos. Transfinite Adams representability, E-print, arXiv :1304.3599v1, [math.AT], [math.CT], 12 April, 2013, pp. 1-52.

228. J. Heller, Motivic strict ring spectra representing semi-topological cohomologytheories, E-print, arXiv:1304.6288v1, [math.AG], [math.AT], 23 April, 2013, pp.1-??, 32Kb.

229. G. Quick, Homotopy theory of smooth compactifications of algebraic varieties,E-print, arXiv:1305.17777, [math.AG], [math.AT], May 8, 2013, pp. 1-10.

230. M. Hoyois, S. Kelly, P. A. Ostvaer, The motivic Steenrod algebra in positivecharacteristic, E-print, arXiv:1305.5690v2, [math.AG], [math.AT], [math.KT],31 July 2013, pp. 1-39.

231. P. Pelaez, Ch. Weibel, Slices of co-operations for KGL, E-print,arXiv:1307.4005v1, [math.AG], [math.KT], 15 July 2013, pp. 1-20.

232. M. Hoyois, Traces and fixed points in stable motivic homotopy theory, E-print,arXiv:1309.6147v1, pp. 1-19, 24 Sept. 2013.

233. K. Ormsby, P. A. Ostvaer, Stable motivic π1 of low dimensional fields, E-print,arXiv:1310.2970v1, pp. 1-27, Oct. 13, 2013.

234. D. Isaksen, From motivic homotopy to classical homotopy: Inverse engeneeringof the clssical Adams-Novikov spectral sequence, a lecture at Stanford, 2013, pp,1-13 (slides).

59

8. APPLICATIONS TO OTHER CLASSES OF

COHOMOLOGY THEORIES

1. S. Geller, Ch, Weibel, Etale Descent for Hochschild and Cyclic cohomology, Com-ment. Math. Helvetici, v. 66 (1991), No. 3, 368-388.

2. T. Goodwillie, S. Lichtenbaum, A cohomological bound for the h-topology, Amer.J. Math., v. 123 (2001), no. 3, pp. 425-443.

3. A. A. Beilinson, S. Bloch, H. Esnault, ǫ-Factors for Gauss-Manin determi-nants, Moskow Math. Journ., 2(2002), no. 3, pp. 477-532; see also http ://www.math.uchicago.edu/ ∼ bloch/bbefinal.ps.

4. I. Panin, Poincare duality for projective varieties, Preprint, June 2002, pp. 1-18,available at the K-theory archive, no. 576.

5. I. Panin, S. Yagunov, Rigidity for orientable functors, J. of Pure and Appl.Algebra, v. 172 (2002), pp. 49-77; see also http : //www.math.uiuc.edu/K −

theory, no. 490, 2001, pp. 1-25.

6. I. Panin, Oriented cohomology theories of algebraic varieties, K-theory, v. 30(2003), pp. 263-312.

7. I. Panin, Push-forward in oriented homology theories of algebraic varieties: II(after Panin and Smirnov), Homology, Homotopy and appl., v. 11(2009), pp.349-405; see also http : //www.math.uiuc.edu/K − theory, no. 619, 2003, pp.1-83.

8. K. Pimenov, Traces in oriented homology theories, Preprint, Oct. 2003, pp. 1-27,available at the K-theory archive http : //www.math.uiuc.edu/K − theory, no.667.

9. K. Pimenov, Traces in oriented homology theories, II, Preprint, 2005, pp. 1-68,available at the K-theory archive, http : //www.math.uiuc.edu/K − theory, no.724.

10. A. Nenashev, Projective bundle theorem in homology theories with Chernstructure, Documenta math., v. 9 (2004), pp. 487-498; see also http ://www.math.uiuc.edu/K − theory, no. 668, pp. 1-9, 2004 (p.488).

11. Th. Geisser, Motivic cohomology, K-theory and topological cyclic homology,Handbook of K-theory, pp. 193-234, see item I-38 above.

12. Th. Geisser, Weil-Etale cohomology over finite fields, Math. Annales, v. 330(2004), no. 4, pp. 662-692; see also arXiv:math.NT/0404425.

13. T. Geisser, The cyclotomic trace map and values of zeta functions, in: Algebraand Number theory, Proc. of the silver jubilee conf., Univ. Hyderabad, 2003,ed. Tandon R., Hidnustan Book agency, Dehli, 2005, pp. 211-225; see alsohttp : //www.math.uiuc.edu/K − theory, no. 697, June 2004, pp. 1-15; orwww.researchgate.net/publications/2113522

60

14. T. Geisser, Arithmetic cohomology over finite fields and special values of zeta-functions, Duke Math. J., 133 (2006), no. 1, 27-57; see also E-print, 2004, pp.1-28, http://www.arXiv.org, no. math.NT/0405164.

15. I. Panin, S. Yagunov, T -spectra and Poincare duality, E-print, available at http ://www.arXiv.org, no. math.AG/0506017, 2005, pp. 1-22.

16. L. Smirnov, Orientations and transfers in cohomology of algebraic varieties, Al-gebra i Analisis, t. 18 (2006), no. 2, pp. 167-224 (in Rus.); English transl.: St.Petersburg Math. J., 18 (2007), no. 3, pp. 305-346.

17. A. Nenashev, K. Zamouline, Oriented cohomology and motivic decompositionsof relative cellular varieties, J. Pure and Appl. Algebra, v. 205 (2006), no, 2, pp.323-340,

18. L. Smirnov, Riemann-Roch theorem for orientations in cohomology of alge-braic varieties, St. Petersburg Math. J., v. 18 (2007), pp. 837-856; see alsohttp://www.ams.org/spmj/2007-18-05/

19. T. Geisser T., L. Hesselholt, The de Rham-Witt complex and p-adic vanishing cy-cles, Journ. AMS, 19 (2006), pp. 1-36; see also http : //www.math.uiuc.edu/K−

theory, no. 615, 2003, pp. 1-40.

20. R. Joshua, Generalized t-structures: t-structures for sheaves of dg-modules overa sheaf of dg-algebras and diagonal t-structures, Preprint, 2006, pp. 1-18, http ://www.math.ohio − state.edu/ ∼ joshua/gent − struct2.pdf .

21. O. Gabber, Notes on some t-structures, in ”Geometric aspects of Dwork the-ory, ed. A. Adolfson, v. II, Walter de Gruyter, Berlin, 2004, pp. 711-734,http : //books.google.com/, or http//www.reference − global.com/doi/pdf//10.1515/9783110198133.2.711?cookieSet=1 (access needs a subscription).

22. D. C., Cisinski, F. Deglise, Kunneth formula, duality and finiteness, Preprint,May, 2006, pp. 1-99, available at http : //www − math.univ − paris13.fr/ ∼

cisinski/main.pdf

23. C. Cisinski, F. Deglise, Mixed Weil cohomology, Advances in Math., 230 (2011),no. 1, pp. 55-130; see also http : //arxiv.org, no. 0712.3291, [math.AG].

24. J. Ayoub, Motives of rigid varieties and the motivic nearby cycles functor, Lec-ture at the Hodge theory conference, Venice, June 2006, pp. 1 - 21, avail-able at https : //convegni.math.unipd.it/hodge/slides/ayoub.pdf or http ://user.math.uzh.ch/ayoub/Other − PDF/V enice Hodge.pdf .

25. J. Ayoub, Motifs des varieties analytiques rigides, E-preptint, Aug. 2008, pp. 1-220, available at the K-theory archive http : //www.math.uiuc.edu/K − theory,no. 907, aug. 27, 2008; an older version http : //www.math.univ−paris13.fr/ ∼

ayoub, pp. 1-107.

26. J. Riou, Dualite (d’apres Offer Gabber), Preprint, 2008, pp. 1-84, http ://www.math.u − psud.fr/ ∼ riou/doc/dualite.pdf .

61

27. L. Illusie, Old and new in etale cohomology, after O. Gabber, a lecture deliv-ered at the Math. Soc. of Japan meeting, Sendai, Sept. 22, 2007, pp. 1-63, slides available at http : //www.ms.u − tokyo.ac.jp/ ∼ t − saito/conf/rv/illusie sendai2.pdf .

28. L. Illusie, Old and new in etale cohomology, after O. Gabber, A summary, pp.1-5, available at http : //www.mcm.ac.cn/B/illusie sendai.pdf

29. L. Illusie, On Gabber’s uniformization theorems: outline and applications to etalecohomology, Lect. delivered at Univ. Tokyo, Sept. 2007, pp. 1-32, available atwww.math.u−psud.fr/ ∼ illusie/refineduniformization3.pdf , or older versionhttp : //www.ms.u − tokyo.ac.jp/ ∼ t − saito/rv/Illusie Tokyo.pdf , pp. 1-8.

30. A. Chatzistamatiou, Etale cohomology of the complement of a linear subspacearrangement, Journal of K-theory, Feb. 2011 (on line), see also E-print, http ://www.arxiv.org, no. 0709.1127v1, [math.AG], Sept. 2007,

31. I. Panin, Oriented cohomology theories of algebraic varieties II, (after I. Paninand A. Smirnov), Homology, Homotopy and applications, vol. 11 (2009), no. 1,pp. 349-405.

32. S. Gorchinsky, A. Rosly, A polar complex of locally free sheaves, E-print, pp.1-36, 26 Jan. 2011, arXiv:1101.5114v1, [math.AG]. pp. 1-???

33. S. Gille, K. Zainoulline, Equivariant pretheories and invariants of tor-sors, Preprint, May, 2011, pp. 1-23, http : //mathematik.uni −

bielefeld.de/lag/man/433.pdf .

34. B. Bhatt, Torsion in the crystaline cohomology of singular varieties, E-print,arXiv:1205.1597v1, [math.AG], May 8, 2012, pp. 1-9.

35. M. Hoyois, Etale symmetric Kunneth theorem, Preprint, 2012, pp. 1-19, availableat: http : //math.northswestern.edu/ ∼ hoyois/papers/etalekunneth.pdf

36. Nguyen Le Dang Thi, Unramified cohomology, A1-connectedness, and Chevalley-Warning problem in Grothendieck ring, Compt. Rend. Acad. Sci. Paris, ser. I,t. 350 (2012), pp. 613-615; see also arXiv:1201:5368v4, [math.AG], pp. 1-4, 13Aug. 2012.

37. A. Krishna, The motivic cobordism for group actions arXiv:1206.5952,[math.AG], June 26, 2012.

38. J. Ross, Cohomology theories with supports, E-print, arXiv:1207.2629v1,[math.AG], pp. 1-26, July 11, 2012.

39. F. Deglise, N. Mazzari, The rigid syntomic ring spectrum, E-print,arXiv:1211.5065, [math.AG], Nov. 21, 2012, pp. 1-???

40. M. Hopkins, G. Quick, Hodge filtered complex bordisms, E-print,arXiv:1212.2173v2, [math.AT], [math.AG], 9 Apr., 2013, pp. 1-36.

41. A. Huber, C. Joerder, Differebtial forms in the h-topology, E-print,

62

arXiv:1305v2, [math.AG], 14 June, 2013, pp. 1-29.

42. J. Nekovar, W. Niziol, Syntomic cohomology and regulators for varieties overp-adic field, with an appendix by F. Deglise, E-print, arXiv:1309.7620v1, pp.1-65, 1 Oct. 2013.

43. M. Levine, Yang Y., Zhao G., Algebraic elliptic cohomology theory and flops, I,E-print, arXiv:1311.2158v1, [math.AG], pp, 1-33, 12 Nov., 2013.

9. APPLICATIONS TO DERIVED AND NON-COMMUTATIVE

ALGEBRAIC GEOMETRY AND STACKS

1. B. Toen, Homotopical and higher categorical structures in algebraic geometry,Habilitation, 2003,

2. J. Lurie, Derived algebraic geometry, Thesis, MIT, 2004, http ://www.math.harvard.edu/ ∼ lurie/papers/DAG.pdf ,

3. B. Toen, G. Vezzosi, Homotopical algebraic geometry I: topos theory, Ad-vances in Math., v. 193 (2005), pp. 257-372, http : //www.dma.unifi.it/vezzosi/papers/hagI.pdf , 2001.

4. B. Toen, G. Vezzosi, Brave New Algebraic geometry and global derived modulispaces of ring spectra, in: ”Elliptic Cohomology: Geometry, Applications andHigher Chromatic analogues”, eds. H. Miller, D. Ravenel, London Math. Soc.Lect. Notes Ser. v. 342, Cambridge Univ. Press, 2007, pp. 325-359; see alsoE-print, http : //www.arXiv.org, math.AT/0309145.

5. J. Lurie, Derived algebraic geometry VII, Spectral schemes, Prpeprint, June,2011, pp. 1-102, http : //www.math.harvard.edu/ ∼ lurie/papers/DAG −

V II.pdf ,

6. J. Lurie, Derived algebraic geometry VIII, Quasi-coherent sheaves andTannaka duality theorems, Preprint, May, 2011, pp. 1-183, http ://www.math.harvard.edu/ ∼ lurie/papers/DAG − V III.pdf .

7. J. Lurie, Derived algebraic geometry IX, Closed immersions, Preprint, June,2011, pp. 1-102, http : //www.math.harvard.edu/ ∼ lurie/papers/DAG −

IX.pdf .

8. J. Lurie, Derived algebraic geometry X, Formal moduli problems, Preprint, Sept.1, 2011, pp. 1-166, http : //www.math.harvard.edu/ ∼ lurie/papers/DAG −

X.pdf .

9. J. Lurie, Derived algebraic geometry XI, Descent theorems, Preprint, Sept. 28,2011, pp. 1-73, http : //www.math.harvard.edu/ ∼ lurie/papers/DAG −

XI.pdf .

10. J. Lurie, Derived algebraic geometry XII, Proper morphisms, completions, and

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the Grothendieck existence theorem, Preprint, Nov. 8, 2011, pp. 1-151, http ://www.math.harvard.edu/ ∼ lurie/papers/DAG − XII.pdf .

11. J. Lurie, Derived algebraic geometry XIII, Rational and p-adic homotopy theo-ries, Pereprint, Dec. 15, 2011, pp. 1-106, http : //www.math.harvard.edu/ ∼

lurie/papers/DAG − XIII.pdf .

12. J. Lurie, Derived algebraic geometry XIV, Representability theorems, Preprint,March 14, 2012, pp. 1-119, http : //www.math.harvard.edu/ ∼

lurie/papers/DAG − XIV.pdf .

13. D. Gaitsgory, Basics of quasi-coherent sheaves on stacks, Preprint, 2011, pp. 1-19,available from http : //www.math.harvard.edu/ ∼ gaisgory/GL/QCohtext.pdf

14. Gaitsgory, Notes on geometric Langlands, Ind-coherent sheaves on stacks, E-print, arXiv:1104.4857v6, [math.AG], pp. 1-103, 5 Feb. 2012,

15. D. Gaitsgory, N. Rosenblum, Notes on geometric Langlands. Crystals and D-modules, arXiv : 1111.2087v2, [math.AG], 20 April, 2012, pp. 1-58.

16. D. Gaitsgory, Sheaves of categories and the notion of 1-affinness, E-print,arXiv:4304v3, [math.AG], 20 July, 2013, pp. 1-97.

17. B. Toen, Derived Azumaya algebras and generators for twisted derived cate-gories, Invent. Math., v. 189 (2012), pp, 581- 652; or E-print, pp. 1-54,arXiv:1002.2599v3, 12 Dec. 2011.

18. Banerjee A., Derived schemes and the field with one element, J. demathematiques pures et appliquees, t. 97 (2012), no. 3, pp. 189-203.

19. P. Pandit, Moduli problems in derived noncommutative geometry, PhD the-sis, U. of Pennsylvania, 2011, pp. 1-138, http : //repository.upenn.edu/edissertations/310.

20. J. Wallbridge, Higher Tannaka duality, dissertation, School of Math,Univ. of Adelaide, Australia, Jan. 2011, (dir. M. Varhese), http ://hdl/handle/net/2440/69436; see also: These, Univ. Toulouse III, July 2011,pp. 1-116, https : //thesesups.ups − tlse.fr/1440/12011TOU30080.pdf.

21. A. Preygel, Thom-Sebastiani and duality for matrix factorizations, E-print, pp.1-71, arXiv:1101.5834v1, 30 Jan. 2011 (app. A).

22. A. Preygel, Thom-Sebastiani and duality for matrix factorizations and resultson higher structures of Hochschild invariants, PhD Thesis, MIT, Jan. 2012, pp.1-150, preview available at http : //dspace.mit.edu/handle/1721.1/73373.

23. I. Iwanari, Tannakization in derived algebraic geometry, E-print, pp. 1-48,arXiv:1112.1761v1, [math.AG], 8 Dec. 2011.

24. I. Iwanari, Bar construction and tanakization, E-print, pp. 1- 43,arXiv:1203.0492v1, [math.CT], Mar. 2, 2012; or RIMS preprint RIMS-1748,May 2012, pp. 1-43.

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25. D. Gepher, J. Kock, Univavalence of locally cartesian closed infinity-categories,E-print, pp. 1-26, arXiv:1208.1749v1, [math.CT], 8 Aug. 2012.

26. Antieau, D. Gepner, Brauer group and etale cohomology in derived algebraicgeometry, arXiv:1210.0290v1, [math.AG], pp. 1-71, 1 Oct. 2012.

27. G. Tabuada, En-regularity implies En−1-regularity, E-print, arXiv:1212.1112v1,[math.AG]. Dec. 5, 2012, pp. 1-???.

28. M. Robalo, Noncommutative motives I: A universal characterization of motivicstable homotopy theory, E-print, arXiv:1206.3645v1, [math.AG], [math.AT], pp.1-65, June 16, 2012.

29. M. Robalo, Noncommutative motives II, K-theory and non-commutative mo-tives, E-print, arXiv:1306.3795, [math.AG], [math.KT], 17 June, 2013, 54pp.

30. M. Robalo, Non-commutative geometry and motives (expository notices), Aug.13. 2013, 14pp., dt.dropboxusercontent.com/u/6173171/ncmotives.pdf .

31. A. Blanc, Topological K-theory and Chern character for non-commutative spaces,E-print, arXiv:1211.7360, [math.KT], [math.AG], 30 Nov. 2012.

32. A. Blanc, Invariants topologiques des espaces non-commutative, Thesis, Univ.Monpellier II, E-print, arXiv:1307.6430, [math.AG], [math.AT], 24 July, 2013,pp???

10. SOME OTHER APPLICATIONS AND CONNECTIONS.

1. S. MacLane, I. Moerdijk, Sheaves in Geometry and Logic, A First Introductionto Topos Theory, University Text, v. (1992), Springer, 630pp.

2. J. Alev. A. Ooms, M. Van den Berg, A class of counter-examples to Gelfand-Kirillov Conjecture, Trans. Amer. Math. Soc., 348 (1996), 1709-1716.

3. V. Drinfeld, Infinite dimensional vector bundles in algebraic geometry: an intro-duction, in: Unity of Mathematics, Proceedings of the conference in honor of the90th birthday of I. M. Gelfand, Cambridge, Mass., Sept. 2003, eds. P. Etingof,V. Retakh, I. M. Singer, Progress in Math., v. 244 (2006), pp. 263-304; see alsohttp : //www.arXiv.org, no. math.AG/0309155, v4.

4. W. D. Gillam, Sites, sheaves and stacks, Brown Univ. Lect. Notes, Dec.13, 2008,136pp, available at http : //www.math.brown.edu/ ∼ wgilliam/notes.pdf

5. W. D. Gillam, Log geometry, course, Brown U., 2009?, 78pp., http ://www.math.brown.edu/ ∼ wgillam/lognotes.pdf ,

6. B. Bhatt, K. Schwede, S. Takagi, The weak ordinarity conjecture and F -singularities, E-print, arXiv:1307.3763v1, [math.AG], [math.CA], July 14, 2013,pp. 1-17, 28Kb.

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