BIBLIOGRAPHY ON THE COMPLETELY DECOMPOSED ...

BIBLIOGRAPHY ON THE COMPLETELY DECOMPOSED
TOPOLOGY AND ITS APPLICATIONS
We list below the works where the completely decomposed topology (or as it is
commonly called now the Nisnevich topology) and various related structures and constructions
have been introduced and developed, as well as the papers where these
constructions 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.
I. Monographs and surveys, pp. 2 - 8.
II. Papers, pp. 8 - 56.
1. The basic constructions, p. 8.
TABLE OF CONTENT
2. Applications to the structure, arithmetic and cohomology of algebraic groups,
pp. 8 - 13.
3. Applications to the higher dimensional class field theory, p. 13-14.
4. Applications to the Algebraic K-theory, pp. 14-22.
5. Applications to a study of algebraic cycles, their intersections and the Picard and
Higher Chow groups, pp. 22-24.
6. Applications to the Theory of Motives and Motivic Cohomology, pp. 24 - 37.
7. Applications to motivic homotopy theories of algebraic varieties and schemes,
pp. 37 - 52.
8. Applications to other classes of cohomology theories, pp. 52-54.
9. Applications to derived algebraic geometry, pp. 54-55.
10. Some other applications and connections, pp. 55-56.
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I. MONOGRAPHS, SURVEYS AND LECTURE NOTES
1. Ye. Nisnevich, Etale Cohomology and arithmetic of semisimple groups, Harvard
Thesis, 1982.
2. Ye. Nisnevich, The Completely Decomposed Topology and its Applications. A
Survey, Preprint, 1992, pp. 1-71.
3. K. Kato, Generalized Class Field Theory, in: ”Proceedings of the
International Congress of Mathematicians, Kyoto, Japan, 1990”, Invited
talk, v.1, pp. 381-394, Berlin, Springer Verlag, 1992; 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,
Proceedings of the Internat. Congress of Mathematicians, Kyoto, Japan,
1990, Invited talk, v.1, pp. 419-428, Berlin, Springer Verlag, 1992; 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 Ktheory
and Algebraic Geometry: Connections with Quadratic Forms and Division
Algebras, 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. Internat.
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. Summer
Reserch Institute on Algebraic Geometry, Santa Cruz, 1995, Proc. Sympos.
in Pure Math., v. 62, Part 1, AMS, Providence, 1998, pp. 329-359; see also
http : //www.math.uchicago.edu/motive.ps
9. E. M. Friedlander, Motivic complexes of Suslin-Voevodsky, Seminaire Bourbaki,
t. 49 (1996/97), exposé 833/01-20, Juin 1997, Asterisque, t. 245 (1998), pp.
355-378; see also http : //www.numdam.org/ARCHIV E/SB... reprinted in
the Handbook of K-theory (see item I-39 below), pp. 1081-1104.
10. B. Kahn, La Conjecture de Milnor (d’apres V. Voevodsky), Seminaire
Bourbaki, 49 (1996/97, exposé 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, A 1 -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 Homology
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, Théorie homotopique des schémas, 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 developments
in 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: Algebraic
K-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 Cohomology,
series Clay Mathematics Monographs, no. 2, Amer. Math. Soc., Providence,
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 written
by P. Deligne), in: Algebraic Topology, The Abel Symposium 2007, Abel
Symposia ser., v. 4, eds. N. Baas, E. Friedlander, P.-A. Ostvaer, Springer,
2009, pp. 355-409, www.springerlink.com/index/u15802237j968222.pdf; see
also http : //www.math.uiuc.edu/K − theory, no. 527, 2001, pp. 1-65; or
arXiv:0805.4436v1, [math.AG], pp. 1-64, 28 May, 2008.
20. S. Mueller-Stach, Algebraic cycle complexes, Basic properties, Proc. Conf. Baniff,
2001?, pp. 1-22, available at http : //hodge.mathematik.uni − mainz.de/ ∼
stefan/papers/baniff.pdf
21. J. Riou, Théorie homotopique des S-schémas, Memoire DEA, Ecole Normale
Superieure, Paris, 2001, pp. 1 - 105, http : //www.eleves.ens.fr : 8080/home/
jriou.
22. F. Morel, An introduction to A 1 -homotopy theory, in: Contemporary development
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, enriched
and 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 mathematical
work 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: Fields
Medalists’ 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 Matematyczne,
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 Hirosima,
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 of
2003/04 (7 lectures), available at http : //www.math.nwu.edu/ ∼ eric/lectures
31. E. Friedlander, Cohomology and K-theory, Lectures at the Institute
Henri 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 the
American Institute of Mathematics, Palo Alto, CA, April, 2004, pp. 1-22, available
at http : //www.aimath.org/WWN/motivesdessins/motivic/pdf.
33. Motives and Homotopy theory of schemes, Arbeitsgemeinschaft mit aktuellen
Thema, Organized by T. Geisser, B. Kahn and F. Morel, Mathematisches
Forschungsinstitut 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, périodes),
Panaramas et synthésis, t. 17, Soc. Math. de France, Paris, 2004, 275pp.
35. J. F. Jardine, Lectures on presheaves of spectra, Univ. of Western Ontario, Fall
Semester 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, 8
lectures, available at http : //www −math.mit.edu/ ∼ tlawson/motivic.html or
http : //www.math.umn.edu/ ∼ tlawson/motivic.html.
38. A. Schmidt, Higher dimensional class field theory (from a topological point of
view), Preprint, 2005, pp. 1-11, 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 der
Mathematishen Wissenschaften, b. 332, Springer, 2006, 507pp., see especially
chapters:
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’iété France- Asiatique de Géométrie
Algébrique et Théorie 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, Uwe
Jannsen, Marc Levine, July 16-22, 2006, Mathematisches Forschungsinstitut
Oberwolfach, report 32/2006, available at http : //www.mfo.de/
programme/schedule/ 2006/29/OWR 2006.32.pdf.
45. F. Morel, A 1 -algebraic topology, in: Proc. Internat. Congress of
Mathemat. (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 at
http : //cmj.dw.uba.ar/Members/gcorti/workgroupswick/en/sedam.pdf; includes
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 at
http : //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, Cambridge
Univ. Press, vols. 343, 344, 2007 (Ayoub J., Barbieri-Viale L., Deglise F., Kahn
B., Moore J. P.).
49. B. Dundas, M. Levine, P. A. Ostvaer, O. Rondigs, V. Voevodsky, Motivic Homotopy
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 homotopy,
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 géométrique,
Cours de M2 donné á Institut de Mathématique de Jussieu, 2006. Notes
rédigées par Benjamin Collas et Ismael Soudéres, pp. 1-52, version du 23
Mai, 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; free
access 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-49
above, 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-49
above, 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 on
Motives, quantum field theory and pseudodifferential operators, June, 2008, notices
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 Géométrie Algébrique: la posterite
mathématique de Grothendieck, IHES, Jan. 9-14, 2009, available at
http : //www.math.uchicago.edu/ ∼ Bloch/talk090108, pp. 1-18.
59. V. P. Snaith, Stable homotopy theory around the Arf-Kervaire invariant, Progress
in 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, 14 lectures, http : //www.math.uwo.ca/ ∼ jardine.
62. D. Asok, Ideas of geometric topology in algebraic geometry or geometric applications
of A 1 -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 item
I-19 above. See also unpublished lecture notes by H. Esnault and M. Levine,
available at http : //www.abelsymposium.no/2007.
64. F. Déglise, 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 constructubilité dans les catégories motiviques,
Groupe de travaile á l’Univ. Paris 13, 2010 (Cisinski Ch., Deglise F.,
Drew B., Kelley S., Pepin-Lalleur S.), Printemps 2010, exposés I - XV, available
at 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 at
www.lcv.ne.jp/ ∼ smaki/en/articles/icm − total.pdf
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68. J. F. Jardine, Local homotopy theory, a book in preparation, Sept. 2011, pp.
1- 223, http : //www.math.uwo.edu/ ∼ jardine/papers/preprints/book.pdf,
860Kb.
69. F. Morel, A 1 -algebraic topology over a field, Lect. Notes in Math., pp. 1-296, to
appear (2011?).
70. Motives and Milnor conjecture, Ecole d’été,i Institut de mathématique de Jussieu,
Paris, Juin 9-17, 2011, Organisateurs: F. Deglise. V. Maillot, J. Wildehause,
http : //motives − 2011.institute.math.jussieu.fr.
II. PAPERS
1. THE BASIC CONSTRUCTIONS.
1. Ye. Nisnevich, Arithmetical and cohomological invariants of semisimple group
schemes and of compactifications of locally symmetric spaces, Functional Analysis
and 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
spectral sequences in the Algebraic K-theory, in: ”Algebraic K-theory: Connections
with Geometry and Topology”, J. F. Jardine and V. Snaith (editors), NATO
Advanced Study Institute Series, Ser. C, v.279, Kluwer,1989, pp. 241-342.
4. Anel M., Grothendick topologies from unique factorization systems, available
at http : //crm.es/Publications/09/Pr847.pdf, pp. 1-67; see also http :
//thales.math.uqam.ca/ ∼ anelm/mat/doc/factorization.pdf.
5. F. Déglise. Introduction á 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 motivic homotopy
theory, with a proof of the motivic tubular neighborhood theorem, Preprint,
2010, pp. 1-16, http : //www.northwestern.edu/ ∼ hoyois
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 homogènes principaux rationnellement triviaux et
arithmétique des schémas en groupes réductifs sur les anneaux de Dedekind,
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Comptes Rendus Academie des Sciences, Paris, t. 299 (1984), No. 1, pp. 5-8.
4. Ye. Nisnevich, On certain arithmetic and cohomological invariants of semisimple
groups, Preprint, 1988, pp. 1-44.
5. Ye. Nisnevich, Generalized integral Iwasawa and Bruhat- Steinberg decompositions
for semisimple group schemes over Dedekind rings, Preprint, 1988, pp.
1-46.
6. Ye. Nisnevich, On the Serre - Grothendieck Conjecture concerning rationally
trivial principal homogeneous spaces, Preprint, 1988, 1-90.
7. Ye. Nisnevich, Espaces homogènes principaux rationnellement triviaux, pureté
et arithmétique des schémas en groupes réductifs sur les extensions des anneaux
locaux réguliers 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 of
arithmetic 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 flasque
tori- Applications, J. Algebra, v. 106 (1987), 148-205.
10. M. Morishita, On S-class number relations for algebraic tori in Galois extensions
of global fields, Nagoya Math. Journ., v. 124 (1991), 131-143.
11. C. Douai, Points rationnelles dans les éspaces homogènes des groupes semi-simple
sur les anneaux de Dedekind, Publ. Inst. Math. Avancee, Lille, 1992, v. 28, No.
IV, pp. 1-17.
12. J.-C. Douai, Espaces homogènes rationnallement triviaux et arithmétique des
schémas en groupes réductifs sur anneau de Dedekind. Comptes Rendus de
Acad. Sciences, Paris, t. 317(1993), pp. 1007 - 1012.
13. P. Gille, Torseurs sur la droit affine et R-equivalence, Thesis, Orsay, 1994?, available
at http : //www.math.u − psud.fr/ ∼ gille/prepublis/doct.pdf; cat.inist.fr
14. J.-C. Douai, Espaces homogènes et arithmétique des schémas en groupes réductifs
sur 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 Rendus
Acad. Sciences, Paris, t. 316(1993), pp. 315-320.
16. B. Mazur, On the passage from local to global in the Number Theory, Bull. of
the 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 real
9

function 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 algébriques réductifs, Publ.
Math.IHES, no. 86 (1997), pp. 199-235.
21. A. Pianzola, Affine Kac-Moody Lie algebras and torsors over the punctured
line, Preprint, 2002, pp. 1-8, available at http : //www.arXiv.org/, no.
math.RT/0203277.
22. K. Zainulin, Hyposis of Grothendieck for principle homogeneous spaces
for 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.
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41. J.-L. Colliot-Thélène, R. Parimala, V. Suresh, Patching and local-global principles
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11

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43. Ch. D., Gonzáles-Avilés, Neron class groups and Tate- Shafarevich groups of
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44. Ch. D. Gonzáles-Avilés, Neron-Raunaud class groups of tori and the capitulation
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45. I. Panin, A. Stavrova, N. Vavilov, On Grothendieck-Serre conjecture concerning
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46. I. Panin, Purity conjecture for reductive groups, Vestnik St. Petersburg U., vol.
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47. J. Ayoub, S. Zucker, Relative Artin motives and reductive Borel-Serre compactifications
of locally symmetric varieties, 3 March, 2011, pp. 1-111, available
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les espaces homogènes, Thèse, 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.
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50. M. Wendt, A 1 -homotopy of Chevalley groups, Journ. of K-theory, v?? (2010),
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51. M. Wendt, On rational A 1 -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,
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53. G. Banaszak, W. Gaida and P. Krason, On the image of Galois ℓ-adic representation
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56. A, Asok, Remarks on smooth A 1 -homotopy groups of smooth toric models, Math.
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58. B. Kahn, Algebraic tori as Nisnevich sheaves with transfers, E-print,
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62. E. Frenkel, Langlands program, trace formulas, and their geometrization, arXiv :
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3. APPLICATION TO THE HIGHER DIMENSIONAL
CLASS FIELD THEORY.
1. K. Kato, S. Saito, Global Class Field Theory of arithmetic Schemes, in: Algebraic
K-theory, Connections with Geometry and Topology?, Contemp. Mathematics,
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2. K. Kato, Conjectures on Etale and Nisnevich Cohomology and L-functions of
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3. K. Kato, A generalization of the Class Field Theory, Sugaky, 40 (1988), pp.
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no. 4, pp. 339-344.
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unpublished manuscript, 1989.
6. S. Saito, Arithmetic Theory of Arithmetic Surfaces, Ann. of Math., 129 (1989),
547-589.
13

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/
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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-5
above.
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 corps
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14. A. Schmidt, Absolute singular homology of arithmetic schemes, Preprint, 2000.
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16. T. Yamasaki, Torsion zero cycles on a product of canonical lifts of elliptic curves,
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20. T. Yamazaki, Brauer-Manin pairing, class field theory and motivic homology,
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14

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 algebraic
cycles and the coniveau filtration, Preprint, 1991, pp. 1-138.
3. R. W. Thomason, Th. Trobauch, Le théoreme de localisation en K-théorie
algébrique, Comptes Rendus Acad. Sciences, Paris, t. 307 (1988), pp. 829-831.
4. R. W. Thomason, Th. Trobauch, Higher algebraic K-theory of schemes and
derived categories, in: ”The Grothendieck Festschrift”, v. III, Progress in Mathematics,
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-Thélène, R. Hoobler, B. Kahn, The Bloch-Ogus -Gabber Theorem,
in: ”Algebraic K-theory, proc. 2nd Great Lake Conf. held at Toronto, 1996”,
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”Algebraic K-theory, Proc. 2nd Great Lake Conf. held in Toronto”, 1996, Fields
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no. 1, pp. 99-138.
9. D. Arlettaz, C. Banaszak, W. Gajda, On Product in algebraic K-theory, Comm.
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10. J. Rognes, C. Weibel, M. Kolster, Two primary algebraic K- theory of rings of
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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 ”Algebra,
Arithmetic, and Geometry”, Proc. Internat. Colloq. Mumbai, 2000), part
I, 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 ramifiée des quadriques, in Izboldin O., Karpenko
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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.
15

14. T. Geisser, L. Hesselholt, K-theory and topological cyclic homology of smooth
schemes over discrete valuation rings, Transact. AMS, v. 358(2004), no. 1, pp.
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15. M. Karoubi , Ch. Weibel, Algebraic and Real K-theory of real varieties, Topology,
42 (2003), no. 4, pp. 715-742; see also http : //www.math.uiuc.edu/K −
theory, no. 473, 2001, pp. 1-37
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18. E. Friedlander, M. Walker, Rational isomorphisms between K- theories and cohomology
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19. P. Balmer, Witt cohomology, Mayer-Vietoris, Homotopy invariance and the
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22. J. Hornbostel, Balmer Witt groups, Karoubi tower and A 1 -homotopy, Preprint,
2002, 13pp., available in http : //www.nwu.edu/faculty
23. V. Voevodsky, A possible approach to the motivic spectral sequence for algebraic
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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 conjectures
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.
16

26. P. Balmer, Introduction to triangular Witt groups and survey of applications,
in: ”Algebraic and Arithmtic theory of quadratic forms”, Proceedings of the
International 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;
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27. C. Haesemeyer, Descent properties for homotopy K-theory, Duke Math. J., v.
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Thélène, S. Garibaldi, R. Sajatha, V. Suresh, Development of math., v. 18,
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29. Cortinas, C. Haesemeyer, M. Schlichting, C. Weibel, Cyclic homology, cdhcohomology
and negative K-theory, Annals of Math., 165 (2007), pp. 1-
25, see also http : //annals.math.princeton.edu/issues/2007/FinalFiles/
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uiuc.edu/K − theory, no. 722.
30. A. Rosenschon, P.-A. Oestvaer, Homotopy limit problem for two- primary algebraic
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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 Jacobians
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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-théorie algébrique et régulateurs via la théorie
homotopique des schémas, Comp. Rend. Acad. Sci. Paris, (2006), pp. ??.
36. J. Riou, Operations on K-théorie algebrique et régulateurs via theorie homotopique
des schemes, Thèse, Univ. Paris VII, July 2006, pp. 1-216, available at
the 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 Winter
17

School 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 others,
in Topics in Algebraic and topological K-theory (Lectures at the Sedano
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//cms.dm.uba.ar/Members/gcorti/workinggroup.swisk/en/sem.pdf.
39. T. Geisser, Parshin’s conjecture revisited, in: K-theory and noncommutative
geometry, eds: G. Cortinas, J. Cuntz, M. Karoubi, R. Nest, C. Weibel, EMS
series 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.
42. B. Kahn, M. Levine, Motive of Severi-Brauer varieties and K-theory of simple
algebras Abel Symposium, Oslo, 2007, pp. 1-57, available at http :
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44. B. Kahn, Homotopical approaches to SK1 and SK2 of central simple
algebras (joint work with Mark Levine), talk at the Conference
on quadratic forms, Utalca, Chile, 2007, available at http :
//people.math.jussieu.fr/ ∼ kahn/preprints/SK1 − LLANquihue.pdf or
inst − mat.utalca.cl/qfc2007/Talks/kahn.pdf
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Block-Kato conjecture, Preprint, pp. 1-13, 2007, available at http :
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46. I.Panin, K. Pimenov, O. Roendigs, On the relation of Voevodsky’s algebraic
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47. G. Cortinas, C. Haesemeyer, M. Walkeri, C. Weibel, The K-theory of toric varieties,
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48. A. Asok, Equivariant vector bundles on certain affine G-varieties, Pure and
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49. A. Asok, B. Doran, Vector bundles on contractible smooth schemes, Duke Math.
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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.
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8. A. Vishik, Integral motives of quadrics, Preprint, MPI-1998-13, pp. 1-
22

82, http : //www.mpim − bonn.mpg.de/preprints/send?bid = 286.ps.
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23

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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.
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the K-theory archive, http : //www.uiuc.edu/K − theory, no. 170, Dec. 1996.
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24

7. C. Weibel, Products in Higher Chow groups and motivic cohomology, in: ”Algebraic
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K-theory. Seattle, 1999”, Proc. Symp. Pure Math., v. 67 (1999), pp. 181-211.
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25

www.math.uiuc.edu/K − theory, no. 378, 2000, pp. 1-4.
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muenster.de/sfb/about/publ/heft154.ps.
32. C. Serpé, A triangulated category of equivariant motives, Preprint, Univ. Munster,
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muenster.de/sfb/publ/heft173
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pp. 1-56.
26

36. S. Borghesi, Stable representability of motivic cohomology, Preprint, 2002.
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2002, pp. 1-19.
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theory, no. 487.
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502.
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Princeton, 1999-2000, 230pp, 2002, (see title I,18) above).
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37

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38

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79. D. Isaksen, Flasque model structure for presheaves, Preprint, Jan. 13, 2004, pp.
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209. Nguyen Le Dang Thi, Unramified cohomology, A 1 -connectedness, and Chevalley-
Warring problem in Grothendieck ring, E-print, pp. 1- 12, arXiv:1201.5368v1,
52

[math.AG], 25 Jan. 2012.
210. 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.
8. APPLICATIONS TO OTHER CLASSES OF
COHOMOLOGY THEORIES
1. S. Geller, Ch, Weibel, Etale Descent for Hochschild and Cyclic cohomology, Comment.
Mathem. Helvetici, v. 66 (1991), No. 3, 368-388.
2. Goodwillie T., Lichtenbaum S., A cohomological bound for the h-topology, Amer.
J. Math., v. 123 (2001), no. 3, pp. 425-443.
3. Beilinson A. A., Bloch S., H. Esnault, ǫ-Factors for Gauss-Manin determinants,
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 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 K-theory archive, http : //www.math.uiuc.edu/K −theory, no. 724.
10. A. Nenashev, Projective bundle theorem in homology theories with Chern
structure, 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.
53

13. T. Geisser, The cyclotomic trace map and values of zeta functions, in Algebra
and Number theory, Proc. of the silver jubilee conf., Univ. Hyderabad, 2003,
ed. Tandon R., Hidnustan Book agency, Dehli, 2005, pp. 211-225; see also
http : //www.math.uiuc.edu/K − theory, no. 697, June 2004, pp. 1-15.
14. T. Geisser, Arithmetic cohomology over finite fields and special values of zetafunctions,
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, Algebra
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 decompositions
of 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 algebraic
varieties, St. Petersburg Math. J., v. 18 (2007), pp. 837-856; see also
http://www.ams.org/spmj/2007-18-05/
19. T. Geisser T., L. Hesselholt, The de Rham-Witt complex and p-adic vanishing cycles,
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 over
a 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 theory,
ed. A. Adolfson, v. II, Berlin, 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 (full, needs a subscription).
22. D. C., Cisinski, F. Déglise, 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. Déglise, 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, Lecture
at the Hodge theory conference, Venice, June 2006, pp. 1 - 21, available
at https : //convegni.math.unipd.it/hodge/slides/ayoub.pdf or http :
//user.math.uzh.ch/ayoub/Other − PDF/V eniceHodge.pdf.
25. J. Ayoub, Motifs des variéties analytiques rigides, E-preptint, Aug. 2008, pp. 1-
220, available at the K-theory archive http : //www.math.uiuc.edu/K −theory,
54

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.
27. L. Illusie, Old and new in etale cohomology, after O. Gabber, a lecture delivered
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 amd new in etale cohomology, after O. Gabber, A summary, pp.
1-5, available at http : //www.mcm.ac.cn/B/illusiesendai.pdf
29. L. Illusie, On Gabber’s uniformization theorems: outline and applications to etale
cohomology, Lect. delivered at Univ. Tokyo, Sept. 2007, pp. 1-32, available at
www.math.u−psud.fr/ ∼ illusie/refineduniformization3.pdf, or older version
http : //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 subspace
arrangement, Journal of K-theory, Feb. 2011 (on line), see also E-print, http :
//www.arxiv.org, no. 0709.1127v1, [math.AG], Sept. 2007,
30. I. Panin, Oriented cohomology theories of algebraic varieties II, (after I. Panin
and A. Smirnov), Homology, Homotopy and applications, vol. 11 (2009), no. 1,
pp. 349-405.
31. S. Gorchinsky, A. Rosly, A polar complex of locally free sheaves, E-print, pp.
1-36, 26 Jan. 2011, arXiv:1101.5114v1, [math.AG].
32. S. Gille, K. Zainoulline, Equivariant pretheories and invariants of torsors,
Preprint, May, 2011, pp. 1-23, http : //mathematik.uni −
bielefeld.de/lag/man/433.pdf.
9. APPLICATIONS TO DERIVED ALGEBRAIC GEOMETRY
AND STACKS
1. J. Lurie, Derived algebraic geometry, Thesis, MIT, 2004, http :
//www.math.haravrd.edu/ ∼ lurie/papers/DAG.pdf,
2. B. Toen, G. Vezzosi, Homotopical algebraic geometry I: topos theory,
Advances in Math., v. 193 (2005), pp. 257-372, http :
//www.dma.unifi.it/vezzosi/papers/hagI.pdf, 2001.
3. B. Toen, G. Vezzosi, Brave New Algebraic geometry and global derived moduli
spaces of ring spectra, in: ”Elliptic Cohomology: Geometry, Applications and
Higher Chromatic analogues”, eds. H. Miller, D. Ravenel, London Math. Soc.
Lect. Notes Ser. v. 342, Cambridge Univ. Press, 2007, pp. 325-359; see also
55

E-print, http : //www.arXiv.org, math.AT/0309145.
4. J. Lurier, Derived algebraic geometry VII, Spectral schemes, 2011, pp. 1-??, Feb.
2011, http : //www.math.haravrd.edu.edu/ ∼ lurie/papers/DAG − V II.pdf,
5. J. Lurie, Derived algebraic geometry X, Formal moduli problems, Nov. 5, 2011,
pp. 1-166, http : //www.math.harvard.edu/ ∼ lurie/papers/DAG − X.pdf.
6. J. Lurie, Derived algebraic geometry XI, Descent theorems, 2011, pp. 1-73,
http : //www.math.harvard.edu/ ∼ lurie/papers/DAG − XI.pdf.
7. J. Lurie, Derived algebraic geometry XII, Proper morphisms, completions,
and the Grothendieck existence theorem, Nov. 8, 2011, pp. 1-151, http :
//www.math.harvard.edu/ ∼ lurie/papers/DAG − XII.pdf.
8. 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
9. D. Gaitsgory, N. Rosenblum, Crystals and D-modules, arXiv : 1111.2087v2,
[math.AG], Nov. 9, 2011, pp. 1-85?.
10. Banergee A., Derived schemes and the field with one element, J. de mathematiques
pures et appliquées, t. 97 (2012), no. 3, pp. 189-203.
11. P. Pandit, Moduli problems in derived nincommutative geometry, Thesis,
U. of Pennsylvania, 2011, pp. 1-138, http : //repository.upenn.edu/
edissertations/310.
12. A. Preygel, Thom-Sebastiani and Duality for matrix factorizations, E-print, pp.
1-71, arXiv:1101.5834v1, 30 Jan. 2011 (app. A).
13. X? Iwanari, Tannakization in derived alg. geometry, E-print, pp. 1-48, arXiv :
1112.1761v1, [math.AG], 8 Dec. 2011.
10. SOME OTHER APPLICATIONS AND CONNECTIONS.
1. S. MacLane, I. Moerdijk, Sheaves in Geometry and Logic, A First Introduction
to 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. Drinfield, Almost projective module and families of Tate spaces, Preprint,
1999.
4. V. Drinfeld, Infinite dimensional vector bundles in algebraic geometry: an introduction,
in: Unity of Mathematics, Proceedings of the conference in honor of the
90th 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 also
http : //www.arXiv.org, no. math.AG/0309155, v4.
56

5. W. D. Gilliam, Sites, sheaves and stacks, Brown Univ. Lect. Notes, Dec.13,
2008, 136pp, available at http : //www.math.brown.edu/ ∼ wgilliam/notes.pdf
6. W. Gilllam, Log geometry, course, Brown U., 2009?, 78pp, http :
//www.math.brown.edu/ ∼ wgillam/lognotes.pdf,
7. J. Ayoub, Une version relative de la conjecture des périodes de Kontsevich-Zagier,
E-print, pp. 1-54?, in K-theory archive, http : //www.math.uiuc.edu/K −
theory, Sept. 4, 2011.
57