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

Mikhail Borovoi

Published 2014-01-23, updated 2021-03-01Version 2

We describe functorially the first Galois cohomology set of a connected reductive algebraic group 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. Here we give a detailed proof.