Equivariant Brauer groups and cohomology

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• 作者：A.M. Cegarra and A.R. Garzó ; n
• 关键词：Cohomology ; Brauer group ; Central simple algebra ; Galois extension ; Ring with operators ; Group of operators
• 刊名：Journal of Algebra
• 出版年：2006
• 出版时间：1 February 2006
• 年：2006
• 卷：296
• 期：1
• 页码：56-74
• 全文大小：157 K

文摘

In this paper we present a cohomological description of the equivariant Brauer group relative to a Galois finite extension of fields endowed with the action of a group of operators. This description is a natural generalization of the classic Brauer–Hasse–Noether's theorem, and it is established by means of a three-term exact sequence linking the relative equivariant Brauer group, the 2nd cohomology group of the semidirect product of the Galois group of the extension by the group of operators and the 2nd cohomology group of the group of operators.