La conjecture de Milnor

Kahn, Bruno

Séminaire Bourbaki : volume 1996/97, exposés 820-834, Astérisque, no. 245 (1997), Exposé no. 834, 40 p.

@incollection{SB_1996-1997__39__379_0,
     author = {Kahn, Bruno},
     title = {La conjecture de {Milnor}},
     booktitle = {S\'eminaire Bourbaki : volume 1996/97, expos\'es 820-834},
     series = {Ast\'erisque},
     note = {talk:834},
     pages = {379--418},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {245},
     year = {1997},
     mrnumber = {1627119},
     zbl = {0916.19001},
     language = {fr},
     url = {http://archive.numdam.org/item/SB_1996-1997__39__379_0/}
}

TY  - CHAP
AU  - Kahn, Bruno
TI  - La conjecture de Milnor
BT  - Séminaire Bourbaki : volume 1996/97, exposés 820-834
AU  - Collectif
T3  - Astérisque
N1  - talk:834
PY  - 1997
SP  - 379
EP  - 418
IS  - 245
PB  - Société mathématique de France
UR  - http://archive.numdam.org/item/SB_1996-1997__39__379_0/
LA  - fr
ID  - SB_1996-1997__39__379_0
ER  -

%0 Book Section
%A Kahn, Bruno
%T La conjecture de Milnor
%B Séminaire Bourbaki : volume 1996/97, exposés 820-834
%A Collectif
%S Astérisque
%Z talk:834
%D 1997
%P 379-418
%N 245
%I Société mathématique de France
%U http://archive.numdam.org/item/SB_1996-1997__39__379_0/
%G fr
%F SB_1996-1997__39__379_0

Kahn, Bruno. La conjecture de Milnor, dans Séminaire Bourbaki : volume 1996/97, exposés 820-834, Astérisque, no. 245 (1997), Exposé no. 834, 40 p. http://archive.numdam.org/item/SB_1996-1997__39__379_0/

Bibliographie
Cité par

[1] J. Arason Cohomologische Invarianten quadratischer Formen, J. Alg. 36 (1975), 448- 491. | DOI | MR | Zbl

[2] M. Artin Brauer-Severi varieties, Lect. Notes in Math. 917, Springer, 1982, 194-210. | MR | Zbl

[3] A. Borel Linear algebraic groups (2e édition), Springer, 1991. | MR | Zbl

[4] A. Bousfield, E. Friedlander Homotopy theory of Γ-spaces, spectra and bisimplicial sets, Lect. Notes in Math. 658, Springer, 1978, 80-130. | MR | Zbl

[5] H. Bass, J. Tate The Milnor ring of a global field, Lect. Notes in Math. 342, Springer, 1973, 349-428. | MR | Zbl

[6] S. Bloch Lectures on algebraic cycles, Duke Univ. Lectures Series, 1982. | MR | Zbl

[7] S. Bloch, K. Kato $p$ -adic étale cohomology, Publ. Math. I.H.E.S. 63 (1986), 107-152. | DOI | EuDML | Numdam | MR | Zbl

[8] F. Châtelet Variations sur un thème de H. Poincaré, Ann. Sci. Ec. Norm. Sup. 61 (1944),249-300. | DOI | EuDML | Numdam | MR | Zbl

[9] M. Demazure Automorphismes et déformations des variétés de Borel, Invent. Math. 39 (1977), 179-186. | DOI | EuDML | MR | Zbl

[10] E. Devinatz, M. Hopkins, J. Smith Nilpotence and stable homotopy theory, I, Ann. of Math. 128 (1988), 207-241. | DOI | MR | Zbl

[11] D. Elman, T. Y. Lam Pfister forms and $K$ -theory of fields, J. Alg. 23 (1972), 181- 213. | DOI | MR | Zbl

[12] E. Friedlander, V. Voevodsky Bivariant cycle cohomology, prépublication, 1995. | Zbl

[13] J.-P. Jouanolou Une suite exacte de Mayer-Vietoris en $K$ -théorie algébrique, Lect. Notes in Math. 341, Springer, 1973, 293-316. | MR | Zbl

[14] K. Kato A generalization of higher class field theory by using $K$ -groups, I, J. Fac. Sci., Univ. Tokyo 26 (1979), 303-376. | MR | Zbl

[15] K. Kato Milnor K-theory and the Chow group of zero cycles, Contemp. Math. 55 (I), AMS, 1986, 241-253. | DOI | MR | Zbl

[16] T. Y. Lam The algebraic theory of quadratic forms (2ème édition), Benjamin, 1980. | MR | Zbl

[17] M. Knebusch Generic splitting of quadratic forms, I, Proc. London Math. Soc. 33 (1976), 65-93. | DOI | MR | Zbl

[18] A. S. Merkurjev Sur le symbole de résidu normique de degré 2 (en russe), Dokl. Akad. Nauk SSSR 261 (1981), 542-547. Traduction anglaise : Soviet Math. Dokl. 24 (1981), 546-551. | MR

[19] A. S. Merkurjev On the norm residue homomorphism for fields, Amer. Math. Soc. Transl. 174 (1996), 49-71. | MR | Zbl

[20] A. S. Merkurjev, A. A. Suslin $K$ -cohomologie des variétés de Severi-Brauer et homomorphisme de résidu normique (en russe), Izv. Akad. Nauk SSSR, 46 (1982), 1011- 1046. Traduction anglaise : Math USSR Izv. 21 (1983), 307-340. | MR | Zbl

[21] A. S. Merkurjev, A. A. Suslin L'homomorphisme de résidu normique de degré 3 (en russe), Izv. Akad. Nauk SSSR 54 (1990), 339-356. Traduction anglaise : Math. USSR Izv. 36 (1991), 349-368. | MR | Zbl

[22] J. Milnor Algebraic $K$ -theory and quadratic forms, Invent. Math. 9 (1970), 315-344. | DOI | EuDML | MR | Zbl

[23] J. Milnor An introduction to algebraic $K$ -theory, Ann. Math. Studies 72, Princeton University Press, 1971. | MR | Zbl

[24] J. Milnor, J. Stasheff Characteristic classes, Ann. Math. Studies 76, Princeton University Press, 1974. | MR | Zbl

[25] F. Morel Théorie de l'homotopie et motifs, I, prépublication, 1995.

[26] F. Morel, V. Voevodsky Homotopy category of schemes over a base, en préparation. | Numdam | Zbl

[27] Y. Nisnevich The completely decomposed topology on schemes and the associated descent spectral sequences in algebraic K-theory, in Algebraic K-theory : connections with geometry and topology, (J.F. Jardine, V.P. Snaith, eds.), NATO ASI Series, Ser. C 279 (1989), 241-342. | MR | Zbl

[28] D. Orlov, A. Vishik, V. Voevodsky Motivic cohomology of Pfister quadrics, en préparation.

[29] D. Quillen Hornotapical algebra, Lect. Notes in Math. 43, Springer, 1967. | MR | Zbl

[30] D. Ravenel Complex cobordism and stable homotopy groups of spheres, Acad. Press, 1986. | MR | Zbl

[31] D. Ravenel The nilpotence and periodicity theorems in stable homotopy theory, Séminaire Bourbaki, juin 1990, exposé n° 728, Astérisque 189-190 (1990), 399-428. | EuDML | Numdam | MR | Zbl

[32] D. Ravenel Nilpotence and periodicity in stable homotopy theory, Ann. Math. Studies 128, Princeton University Press, 1992. | MR | Zbl

[33] M. Rost Hilbert's theorem 90 for $K_{3}^{M}$ for degree-two extensions, prépublication, 1986.

[34] M. Rost On the spinornorm and $A_{0} (X, K_{1})$ for quadrics, prépublication, 1988.

[35] M. Rost Some new results on the Chowgroups of quadrics, prépublication, 1990.

[36] M. Rost Chow groups with coefficients, Documenta Math. 1 (1996), 319-393. | EuDML | MR | Zbl

[37] D. Saltman Retract rational fields and cyclic Galois extensions, Isr. J. Math. 47 (1984),165-215. | DOI | MR | Zbl

[38] J.-P. Serre Cohomologie galoisienne (nouvelle édition), Lect. Notes in Math. 5, Springer, 1994. | MR | Zbl

[39] C. Soulé $K_{2}$ et le groupe de Brauer, Séminaire Bourbaki, novembre 1982, exposé n° 601, Astérisque 105-106 (1983), 79-93. | EuDML | Numdam | MR | Zbl

[40] N. Spaltenstein, Resolutions of unbounded complexes, Compositio Math. 65 (1988), 121-154. | EuDML | Numdam | MR | Zbl

[41] A. Suslin L'homomorphisme quaternionique pour le corps des fonctions d'une conique (en russe), Dokl. Akad. Nauk SSSR. 265 (1982), 292-296. Traduction anglaise : Soviet Math. Dokl. 26 (1982), 72-77. | MR | Zbl

[42] A. Suslin, V. Voevodsky Bloch-Kato conjecture and motivic cohomology with finite coefficients, prépublication, 1995. | Zbl

[43] J. Tate Relations between $K_{2}$ and Galois cohomology, Invent. Math. 36 (1976), 257- 274. | DOI | EuDML | MR | Zbl

[44] V. Voevodsky Homology of schemes, II, prépublication, 1993. | Zbl

[45] V. Voevodsky Triangulated categories of motives over a field, prépublication, 1994. | Zbl

[46] V. Voevodsky Bloch-Kato conjecture for $𝐙 / 2$ -coefficients and algebraic Morava K-theories, prépublication, 1995.

[47] V. Voevodsky Cohomological operations in motivic cohomology, en préparation. | Zbl

[48] V. Voevodsky The Milnor conjecture, prépublication, 1996.

[49] A. Wadsworth Merkurjev's elementary proof of Merkurjev's theorem, Contemp. Math. 55 (II), AMS, 1986, 741-776. | DOI | MR | Zbl

[50] S. Wang On the commutator subgroup of a simple algebra, Amer. J. Math. 72 (1950), 323-334. | DOI | MR | Zbl