Galois cohomology and the Brauer group of local fields. (English. Russian original) Zbl 0731.11064

Parshin, A. N.

Proc. Steklov Inst. Math. 183, 191-201 (1991); translation from Tr. Mat. Inst. Steklova 183, 159-169 (1990).

This paper completes the author’s project on \(n\)-dimensional local fields begun in an earlier paper [Tr. Mat. Inst. Steklova 165, 143–170 (1984; Zbl 0535.12013)]. The main result here is a computation of the Brauer group of an \(n\)-dimensional local field of characteristic \(p\neq 0\).

Reviewer: K.Szymiczek (Tychy)

MSC:

11S31	Class field theory; \(p\)-adic formal groups
12G05	Galois cohomology
12G10	Cohomological dimension of fields
11S70	\(K\)-theory of local fields
14F22	Brauer groups of schemes
11S25	Galois cohomology
11S15	Ramification and extension theory

Keywords:

higher dimensional local fields; Brauer group

Citations:

Zbl 0535.12013