Milnor’s conjecture on quadratic forms and motivic complexes
Rendiconti del Seminario Matematico della Università di Padova (2005)
- Volume: 114, page 63-101
- ISSN: 0041-8994
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topMorel, Fabien. "Milnor’s conjecture on quadratic forms and $~mod \ ; 2$ motivic complexes." Rendiconti del Seminario Matematico della Università di Padova 114 (2005): 63-101. <http://eudml.org/doc/108669>.
@article{Morel2005,
author = {Morel, Fabien},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
language = {eng},
pages = {63-101},
publisher = {Seminario Matematico of the University of Padua},
title = {Milnor’s conjecture on quadratic forms and $~mod \ ; 2$ motivic complexes},
url = {http://eudml.org/doc/108669},
volume = {114},
year = {2005},
}
TY - JOUR
AU - Morel, Fabien
TI - Milnor’s conjecture on quadratic forms and $~mod \ ; 2$ motivic complexes
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 2005
PB - Seminario Matematico of the University of Padua
VL - 114
SP - 63
EP - 101
LA - eng
UR - http://eudml.org/doc/108669
ER -
References
top- [1] J. ARASON, Cohomologische Invarianten Quadratischer Formen. J. Algebra, 36 no. 3 (1975), pp. 448-491. Zbl0314.12104MR389761
- [2] J. K. ARASON - R. ELMAN, Powers of the fundamental ideal in the Witt ring, Journal of Algebra, 239 (2001), pp. 150-160. Zbl0990.11021MR1827878
- [3] P. BALMER - S. GILLE - I. PANIN - C. WALTER, The Gersten conjecture on Witt groups in the equicharacteristic case, Documenta Mathematica 7 (2002), pp. 203-217. Zbl1015.19002MR1934649
- [4] J. BARGE - F. MOREL, Cohomologie des groupes linéaires, K-théorie de Milnor et groupes de Witt. C. R. Acad. Sci. Paris Série I Math., 328 no. 3 (1999), pp. 191-196. Zbl0944.20027MR1674598
- [5] H. BASS - J. TATE, The Milnor ring of a global field. Algebraic K-theory, II: ``Classical'' algebraic K-theory and connections with arithmetic (Proc. Conf., Seattle, Wash., Battelle Memorial Inst., 1972), pp. 349-446. Lecture Notes in Math., Vol. 342, Springer, Berlin, 1973. Zbl0299.12013MR442061
- [6] J.-L. COLLIOT-THÉLÈNE - R. T. HOOBLER - B. KAHN, The Bloch-Ogus-Gabber theorem. Algebraic K-theory (Toronto, ON, 1996), pp. 31-94, Fields Inst. Commun., 16, Amer. Math. Soc., Providence, RI, 1997. Zbl0911.14004MR1466971
- [7] F. DÉGLISE, Modules homotopiques avec transferts et motifs génériques. Thèse de l'université Paris VII, disponible à: http://www-math.univ-paris13.fr/Ädeglise/these.html
- [8] P. ELBAZ-VINCENT - S. MÜLLER-STACH, Milnor K-theory of rings, higher Chow groups and applications, Inventiones Math., 148 (2002), pp. 177-206. Zbl1027.19004MR1892848
- [9] S. GARIBALDI - A. MERKURJEV - J.-P. SERRE, Cohomological Invariants in Galois Cohomology, University Lecture series, volume 28, AMS. Zbl1159.12311
- [10] A. GROTHENDIECK, Sur quelques points d'algèbre homologique, Tohoku Math. J., (2) 9 (1957), pp. 119-221. Zbl0118.26104MR102537
- [11] B. KAHN - R. SUJATHA, Motivic cohomology and unramified cohomology of quadrics. J. Eur. Math. Soc. (JEMS), 2 no. 2 (2000), pp. 145-177. Zbl1066.11015MR1763303
- [12] K. KATO, A generalization of local class field theory by using K-groups. II. J. Fac. Sci. Univ. Tokyo Sect. IA Math., 27 no. 3 (1980), pp. 603-683. Zbl0463.12006MR603953
- [13] K. KATO, Milnor K-theory and the Chow group of zero cycles. Applications of algebraic K-theory to algebraic geometry and number theory, Part I, II (Boulder, Colo., 1983), pp. 241-253, Contemp. Math., 55, Amer. Math. Soc., Providence, RI, 1986. Zbl0603.14009MR862638
- [14] M.-A. KNUS, Quadratic and Hermitian forms over rings. With a foreword by I. Bertuccioni. Grundlehren der Mathematischen Wissenschaften, 294. Springer-Verlag, Berlin, 1991. Zbl0756.11008MR1096299
- [15] J. MILNOR, Algebraic K-theory and Quadratic Forms, Inventiones Math., 9 (1970), pp. 318-344. Zbl0199.55501MR260844
- [16] F. MOREL, Suite spectrale d'Adams et invariants cohomologiques des formes quadratiques, C.R. Acad. Sci. Paris, t. 328, Série I (1999), pp. 963-968. Zbl0937.19002MR1696188
- [17] F. MOREL, Sur les puissances de l'idéal fondamental de l'anneau de Witt, Commentarii Mathematici Helvetici, 79 no. 4 (2004), pp. 689-703. Zbl1061.19001MR2099118
- [18] F. MOREL, The stable A1 -connectivity theorems, to appear in K-theory Journal. Zbl1117.14023MR2240215
- [19] F. MOREL, Milnor's conjecture on quadratic forms and the operation Sq2 , in preparation.
- [20] F. MOREL - V. VOEVODSKY, A1 -homotopy theory of schemes. Inst. Hautes Études Sci. Publ. Math., No. 90 (1999), pp. 45-143. Zbl0983.14007MR1813224
- [21] Y. NISNEVICH, The completely decomposed topology on schemes and associated descent spectral sequences in algebraic K-theory. Algebraic K-theory: connections with geometry and topology (Lake Louise, AB, 1987), 241-342, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 279, Kluwer Acad. Publ., Dordrecht, 1989. Zbl0715.14009MR1045853
- [22] M. OJANGUREN - I. PANIN, A purity theorem for the Witt group. Ann. Sci. École Norm. Sup. (4), 32 no. 1 (1999), pp. 71-86. Zbl0980.11025MR1670591
- [23] D. ORLOV - A. VISHIK - V. VOEVODSKY, An exact sequence for Milnor's K-theory with applications to quadratic forms, preprint, 2000, available at http://www.math.uiuc.edu/K-theory/0454/ Zbl1124.14017
- [24] M. ROST, Chow groups with coefficients. Doc. Math., 1 No. 16 (1996), pp. 319-393 (electronic). Zbl0864.14002MR1418952
- [25] W. SCHARLAU, Quadratic and Hermitian forms. Grundlehren der Mathematischen Wissenschaften, 270 (Springer-Verlag, Berlin, 1985). Zbl0584.10010MR770063
- [26] M. SCHMIDT, Wittringhomologie, Dissertation, Universität Regensburg, 1998.
- [27] A. SUSLIN - V. VOEVODSKY, Bloch-Kato conjecture and motivic cohomology with finite coefficients. The arithmetic and geometry of algebraic cycles (Banff, AB, 1998), pp. 117-189, NATO Sci. Ser. C Math. Phys. Sci., 548, Kluwer Acad. Publ., Dordrecht, 2000. Zbl1005.19001MR1744945
- [28] V. VOEVODSKY, Triangulated categories of motives over a field. Cycles, transfers, and motivic homology theories, pp. 188-238, Ann. of Math. Stud., 143, Princeton Univ. Press, Princeton, NJ, 2000. Zbl1019.14009MR1764202
- [29] V. VOEVODSKY, Cohomological theory of presheaves with transfers. Cycles, transfers, and motivic homology theories, pp. 87-137, Ann. of Math. Stud., 143, Princeton Univ. Press, Princeton, NJ, 2000. Zbl1019.14010MR1764200
- [30] V. VOEVODSKY, Motivic cohomology groups are isomorphic to higher Chow groups in any characteristic, Int. Math. Res. Not., No. 7 (2002), pp. 351-355. Zbl1057.14026MR1883180
- [31] V. VOEVODSKY, Reduced power operations in motivic cohomology, Inst. Hautes Études Sci. Publ. Math., No. 98 (2003), pp. 1-57. Zbl1057.14027MR2031198
- [32] V. VOEVODSKY, Motivic cohomology with Z/2-coefficients, Inst. Hautes Études Sci. Publ. Math., No. 98 (2003), pp. 59-104. Zbl1057.14028MR2031199
- [33] V. VOEVODSKY, The Milnor conjecture, preprint, 1996, available at http://www.math.uiuc.edu/K-theory/0170/
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