Bulletin of the Belgian Mathematical Society - Simon Stevin

Equivariant group cohomology and Brauer group

A. M. Cegarra and A.R. Garzón

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Abstract

In this paper we prove that, for any Galois finite field extension $F/K$ on which a separated group of operators $\Gamma$ is acting, there is an isomorphism between the group of equivariant isomorphism classes of finite dimensional central simple $K$-algebras endowed with a $\Gamma$-action and containing $F$ as an equivariant strictly maximal subfield and the second equivariant cohomology group of the Galois group of the extension.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 10, Number 3 (2003), 451-459.

Dates
First available in Project Euclid: 12 September 2003

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1063372349

Mathematical Reviews number (MathSciNet)
MR2017455

Zentralblatt MATH identifier
1036.12002

Subjects
Primary: 12G05: Galois cohomology [See also 14F22, 16Hxx, 16K50] 16H05: Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) 16K50: Brauer groups [See also 12G05, 14F22] 20J06: Cohomology of groups

Keywords
Group cohomology Brauer group Azumaya algebra Galois extension group of operators

Citation

Cegarra, A. M.; Garzón, A.R. Equivariant group cohomology and Brauer group. Bull. Belg. Math. Soc. Simon Stevin 10 (2003), no. 3, 451--459. https://projecteuclid.org/euclid.bbms/1063372349


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