Soit un groupe réductif connexe sur un corps de nombres , et soit un ensemble (fini ou infini) de places de . On donne une condition nécessaire et suffisante pour la surjectivité de l’application de localisation de vers la « somme directe » des ensembles , où parcourt . Dans les appendices on donne une nouvelle construction de la cohomologie galoisienne abélienne d’un groupe réductif sur un corps de caractéristique quelconque.
Let be a connected reductive group over a number field , and let be a set (finite or infinite) of places of . We give a necessary and sufficient condition for the surjectivity of the localization map from to the “direct sum” of the sets where runs over . In the appendices, we give a new construction of the abelian Galois cohomology of a reductive group over a field of arbitrary characteristic.
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@article{CRMATH_2023__361_G9_1401_0,
author = {Mikhail Borovoi},
title = {Criterion for surjectivity of localization in {Galois} cohomology of a reductive group over a number field},
journal = {Comptes Rendus. Math\'ematique},
pages = {1401--1414},
publisher = {Acad\'emie des sciences, Paris},
volume = {361},
year = {2023},
doi = {10.5802/crmath.455},
language = {en},
}
TY - JOUR AU - Mikhail Borovoi TI - Criterion for surjectivity of localization in Galois cohomology of a reductive group over a number field JO - Comptes Rendus. Mathématique PY - 2023 SP - 1401 EP - 1414 VL - 361 PB - Académie des sciences, Paris DO - 10.5802/crmath.455 LA - en ID - CRMATH_2023__361_G9_1401_0 ER -
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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