Criterion for surjectivity of localization in Galois cohomology of a reductive group over a number field
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 $S$....
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Académie des sciences
2023-11-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.455/ |
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| author | Borovoi, Mikhail |
| author_facet | Borovoi, Mikhail |
| author_sort | Borovoi, Mikhail |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-9273604bf156488cb85406008d62ebbc |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2023-11-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-9273604bf156488cb85406008d62ebbc2025-02-07T11:10:50ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-11-01361G91401141410.5802/crmath.45510.5802/crmath.455Criterion for surjectivity of localization in Galois cohomology of a reductive group over a number fieldBorovoi, Mikhail0Raymond and Beverly Sackler School of Mathematical Sciences, Tel Aviv University, 6997801 Tel Aviv, IsraelLet $G$ 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.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.455/ |
| spellingShingle | Borovoi, Mikhail Criterion for surjectivity of localization in Galois cohomology of a reductive group over a number field Comptes Rendus. Mathématique |
| title | Criterion for surjectivity of localization in Galois cohomology of a reductive group over a number field |
| title_full | Criterion for surjectivity of localization in Galois cohomology of a reductive group over a number field |
| title_fullStr | Criterion for surjectivity of localization in Galois cohomology of a reductive group over a number field |
| title_full_unstemmed | Criterion for surjectivity of localization in Galois cohomology of a reductive group over a number field |
| title_short | Criterion for surjectivity of localization in Galois cohomology of a reductive group over a number field |
| title_sort | criterion for surjectivity of localization in galois cohomology of a reductive group over a number field |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.455/ |
| work_keys_str_mv | AT borovoimikhail criterionforsurjectivityoflocalizationingaloiscohomologyofareductivegroupoveranumberfield |