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arXiv · 1401.5913

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

Mikhail Borovoi
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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.

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Mikhail Borovoi. 2014-01-23. Galois cohomology of reductive algebraic groups over the field of real numbers. https://doi.org/10.46298/cm.9298

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