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

Mikhail Borovoi*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We describe functorially the first Galois cohomology set H1 (R, G) of a connected reductive algebraic group G over the field 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 [3]. Here we give a detailed proof and a few examples.

Original languageEnglish
Pages (from-to)191-201
Number of pages11
JournalCommunications in Mathematics
Volume30
Issue number3
DOIs
StatePublished - 2022

Funding

FundersFunder number
Hermann Minkowski Center for Geometry

    Keywords

    • Galois cohomology
    • real algebraic group

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