\(K_ 2\) et le groupe de Brauer. [d’après A. S. Merkurjev et A. A. Suslin]. (French) Zbl 0535.14005

Soulé, Christophe

Sémin. Bourbaki, 35e année, 1980/81, Exp. 601, Astérisque 105-106, 79-93 (1983).

The paper contains an exposition of the remarkable results of A. S. Merkur’ev and A. A. Suslin [Izv. Akad. Nauk SSSR, Ser. Mat. 46, No.5, 1011-1046 (1982; Zbl 0525.18008), Proc. Steklov. Inst. Math., 165 (1984)] and their applications to algebraic cycles [J.-L. Colliot- Thélène, Invent. Math. 71, 1-20 (1983; Zbl 0527.14011); J.-L. Colliot-Thélène, J. J. Sansuc and the author, C. R. Acad. Sci., Paris, Sér. I 294, 749-752 (1982)].
For the entire collection see [Zbl 0514.00009].

Reviewer: Yu.G.Zarhin

MSC:

14C35	Applications of methods of algebraic \(K\)-theory in algebraic geometry
14F22	Brauer groups of schemes
18F25	Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects)
12G05	Galois cohomology

Keywords:

Galois cohomology; cohomology of Severi-Brauer varieties; Brauer group; \(K_ 2\); algebraic cycles

Citations:

Zbl 0525.18008; Zbl 0527.14011