Milnor’s conjecture on quadratic forms and $mod;2$ motivic complexes

Morel, Fabien

Rendiconti del Seminario Matematico della Università di Padova, Tome 114 (2005), pp. 63-101

[1] J. Arason, Cohomologische Invarianten Quadratischer Formen. J. Algebra, 36 no. 3 (1975), pp. 448-491. | Zbl | MR

[2] J. K. Arason - R. Elman, Powers of the fundamental ideal in the Witt ring, Journal of Algebra, 239 (2001), pp. 150-160. | Zbl | MR

[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. | Zbl | MR

[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. | Zbl | MR

[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. | Zbl | MR

[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. | Zbl | MR

[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. | Zbl | MR

[9] S. Garibaldi - A. Merkurjev - J.-P. Serre, Cohomological Invariants in Galois Cohomology, University Lecture series, volume 28, AMS. | Zbl

[10] A. Grothendieck, Sur quelques points d'algèbre homologique, Tohoku Math. J., (2) 9 (1957), pp. 119-221. | Zbl | MR

[11] B. Kahn - R. Sujatha, Motivic cohomology and unramified cohomology of quadrics. J. Eur. Math. Soc. (JEMS), 2 no. 2 (2000), pp. 145-177. | Zbl | MR | EuDML

[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. | Zbl | MR

[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. | Zbl | MR

[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. | Zbl | MR

[15] J. Milnor, Algebraic K-theory and Quadratic Forms, Inventiones Math., 9 (1970), pp. 318-344. | Zbl | MR | EuDML

[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. | Zbl | MR

[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. | Zbl | MR

[18] F. Morel, The stable A1 -connectivity theorems, to appear in K-theory Journal. | Zbl | MR

[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. | Numdam | Zbl | MR | EuDML

[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. | Zbl | MR

[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. | Numdam | Zbl | MR | EuDML

[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/

[24] M. Rost, Chow groups with coefficients. Doc. Math., 1 No. 16 (1996), pp. 319-393 (electronic). | Zbl | MR | EuDML

[25] W. Scharlau, Quadratic and Hermitian forms. Grundlehren der Mathematischen Wissenschaften, 270 (Springer-Verlag, Berlin, 1985). | Zbl | MR

[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. | Zbl | MR

[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. | Zbl | MR

[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. | Zbl | MR

[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. | Zbl | MR

[31] V. Voevodsky, Reduced power operations in motivic cohomology, Inst. Hautes Études Sci. Publ. Math., No. 98 (2003), pp. 1-57. | Numdam | Zbl | MR | EuDML

[32] V. Voevodsky, Motivic cohomology with Z/2-coefficients, Inst. Hautes Études Sci. Publ. Math., No. 98 (2003), pp. 59-104. | Numdam | Zbl | MR | EuDML

[33] V. Voevodsky, The Milnor conjecture, preprint, 1996, available at http://www.math.uiuc.edu/K-theory/0170/