Mikhail Borovoi - Galois cohomology of reductive algebraic groups over the field of real numbers

cm:9298 - Communications in Mathematics, January 3, 2023, Volume 30 (2022), Issue 3 (Special issue: in memory of Arkady Onishchik) - https://doi.org/10.46298/cm.9298
Galois cohomology of reductive algebraic groups over the field of real numbersArticle

Authors: Mikhail Borovoi

    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.

    Comment: 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


    Volume: Volume 30 (2022), Issue 3 (Special issue: in memory of Arkady Onishchik)
    Published on: January 3, 2023
    Accepted on: June 11, 2022
    Submitted on: April 4, 2022
    Keywords: Mathematics - Group Theory, Mathematics - Number Theory, 11E72, 20G20

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