{"docId":9298,"paperId":9298,"url":"https:\/\/cm.episciences.org\/9298","doi":"10.46298\/cm.9298","journalName":"Communications in Mathematics","issn":"1804-1388","eissn":"2336-1298","volume":[{"vid":631,"name":"Volume 30 (2022), Issue 3 (Special issue: in memory of Arkady Onishchik)"}],"section":[],"repositoryName":"arXiv","repositoryIdentifier":"1401.5913","repositoryVersion":5,"repositoryLink":"https:\/\/arxiv.org\/abs\/1401.5913v5","dateSubmitted":"2022-04-04 14:14:40","dateAccepted":"2022-06-11 16:54:08","datePublished":"2023-01-03 12:57:41","titles":["Galois cohomology of reductive algebraic groups over the field of real numbers"],"authors":["Borovoi, Mikhail"],"abstracts":["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"],"keywords":["Mathematics - Group Theory","Mathematics - Number Theory","11E72, 20G20"]}