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arXiv:2303.04120 [math.NT]AbstractReferencesReviewsResources

Galois cohomology of reductive groups over global fields

Mikhail Borovoi, Tasho Kaletha

Published 2023-03-07, updated 2023-06-12Version 3

Generalizing Tate's results for tori, we give closed formulas for the abelian Galois cohomology groups H^1_{ab}(F,G) and H^2_{ab}(F,G) of a connected reductive group G over a global field F, and obtain formulas, suitable for computer calculatios, for the first nonabelian Galois cohomology set H^1(F,G) of G and for the second Galois cohomology group H^2(F,T) of an F-torus T.

Comments: V1,2: 43 pages. V3: 58 pages, a new section added
Categories: math.NT, math.AG, math.GR, math.RT
Subjects: 11E72, 20G10, 20G25, 20G30
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