Comptes Rendus
Algebra, Number theory
Criterion for surjectivity of localization in Galois cohomology of a reductive group over a number field
Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1401-1414.

Let G be a connected reductive group over a number field F, and let S be a set (finite or infinite) of places of F. We give a necessary and sufficient condition for the surjectivity of the localization map from H 1 (F,G) to the “direct sum” of the sets H 1 (F v ,G) where v runs over S. In the appendices, we give a new construction of the abelian Galois cohomology of a reductive group over a field of arbitrary characteristic.

Soit G un groupe réductif connexe sur un corps de nombres F, et soit S un ensemble (fini ou infini) de places de F. On donne une condition nécessaire et suffisante pour la surjectivité de l’application de localisation de H 1 (F,G) vers la « somme directe » des ensembles H 1 (F v ,G), où v parcourt S. Dans les appendices on donne une nouvelle construction de la cohomologie galoisienne abélienne d’un groupe réductif sur un corps de caractéristique quelconque.

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DOI: 10.5802/crmath.455
Classification: 11E72, 20G10, 20G20, 20G25, 20G30
Mikhail Borovoi 1

1 Raymond and Beverly Sackler School of Mathematical Sciences, Tel Aviv University, 6997801 Tel Aviv, Israel
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Mikhail Borovoi. Criterion for surjectivity of localization in Galois cohomology of a reductive group over a number field. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1401-1414. doi : 10.5802/crmath.455. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.455/

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