Galois cohomology of reductive algebraic groups over the field of real numbers

Abstract

We describe functorially the first Galois cohomology set $H^1(\mathbb{R},G)$ of a connected reductive algebraic group $G$ over the field $\mathbb{R}$ of real numbers in terms of a certain action of the Weyl group on the real points of order dividing 2 of the maximal torus containing a maximal compact torus. This result was announced with a sketch of proof in the author's 1988 note. Here we give a detailed proof.

V.1, v.2, v.3: 6 pages. V.4, v.5: 11 pages, the final version to appear in Communicationa in Mathematics. In this final version, Theorem 9 (the main result) of versions 1-3 became Theorem 3.1

References in corpus (2)

• Galois Cohomology of Real Groups
• Galois cohomology and component group of a real reductive group

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