## 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 numbers

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.

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