Groupes de Brauer algébriques modulo les constantes d’espaces homogènes et leurs compactifications
Let $X$ be a smooth, geometrically integral variety without non-constant invertible functions over a field $K$. Then the quotient of the “algebraic” Brauer group of $X$ by $\mathrm{Br}\,K$ injects into $\mathrm{H}^1(K,\mathrm{Pic}{\overline{X}})$. We show that this inclusion is not always an isomorp...
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Académie des sciences
2024-07-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.587/ |
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| author | Linh, Nguyen Manh |
| author_facet | Linh, Nguyen Manh |
| author_sort | Linh, Nguyen Manh |
| collection | DOAJ |
| description | Let $X$ be a smooth, geometrically integral variety without non-constant invertible functions over a field $K$. Then the quotient of the “algebraic” Brauer group of $X$ by $\mathrm{Br}\,K$ injects into $\mathrm{H}^1(K,\mathrm{Pic}{\overline{X}})$. We show that this inclusion is not always an isomorphism, even in the case where $X$ is a homogeneous space of a connected linear algebraic group over $K$. A similar result for the smooth compactifications of $X$ is also given. |
| format | Article |
| id | doaj-art-597af272353f4feb908c988b0cdad3e6 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2024-07-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-597af272353f4feb908c988b0cdad3e62025-02-07T11:21:52ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-07-01362G669370010.5802/crmath.58710.5802/crmath.587Groupes de Brauer algébriques modulo les constantes d’espaces homogènes et leurs compactificationsLinh, Nguyen Manh0Laboratoire de Mathématiques d’Orsay, Bâtiment 307, rue Michel Magat, Faculté des Sciences d’Orsay, Université Paris-Saclay, F-91405 Orsay Cedex, FranceLet $X$ be a smooth, geometrically integral variety without non-constant invertible functions over a field $K$. Then the quotient of the “algebraic” Brauer group of $X$ by $\mathrm{Br}\,K$ injects into $\mathrm{H}^1(K,\mathrm{Pic}{\overline{X}})$. We show that this inclusion is not always an isomorphism, even in the case where $X$ is a homogeneous space of a connected linear algebraic group over $K$. A similar result for the smooth compactifications of $X$ is also given.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.587/ |
| spellingShingle | Linh, Nguyen Manh Groupes de Brauer algébriques modulo les constantes d’espaces homogènes et leurs compactifications Comptes Rendus. Mathématique |
| title | Groupes de Brauer algébriques modulo les constantes d’espaces homogènes et leurs compactifications |
| title_full | Groupes de Brauer algébriques modulo les constantes d’espaces homogènes et leurs compactifications |
| title_fullStr | Groupes de Brauer algébriques modulo les constantes d’espaces homogènes et leurs compactifications |
| title_full_unstemmed | Groupes de Brauer algébriques modulo les constantes d’espaces homogènes et leurs compactifications |
| title_short | Groupes de Brauer algébriques modulo les constantes d’espaces homogènes et leurs compactifications |
| title_sort | groupes de brauer algebriques modulo les constantes d espaces homogenes et leurs compactifications |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.587/ |
| work_keys_str_mv | AT linhnguyenmanh groupesdebraueralgebriquesmodulolesconstantesdespaceshomogenesetleurscompactifications |