Picard Groups of Algebraic Groups and an Affineness Criterion
We prove that an algebraic group over a field $k$ is affine precisely when its Picard group is torsion, and show that in this case the Picard group is finite when $k$ is perfect, and the product of a finite group of order prime to $p$ and a $p$-primary group of finite exponent when $k$ is imperfect...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2023-02-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.419/ |
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| author | Rosengarten, Zev |
| author_facet | Rosengarten, Zev |
| author_sort | Rosengarten, Zev |
| collection | DOAJ |
| description | We prove that an algebraic group over a field $k$ is affine precisely when its Picard group is torsion, and show that in this case the Picard group is finite when $k$ is perfect, and the product of a finite group of order prime to $p$ and a $p$-primary group of finite exponent when $k$ is imperfect of characteristic $p$. |
| format | Article |
| id | doaj-art-c930b04ec28c47a9874e245501752fa7 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2023-02-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-c930b04ec28c47a9874e245501752fa72025-02-07T11:06:36ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-02-01361G255956410.5802/crmath.41910.5802/crmath.419Picard Groups of Algebraic Groups and an Affineness CriterionRosengarten, Zev0Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Edmond J. Safra Campus, 91904, Jerusalem, IsraelWe prove that an algebraic group over a field $k$ is affine precisely when its Picard group is torsion, and show that in this case the Picard group is finite when $k$ is perfect, and the product of a finite group of order prime to $p$ and a $p$-primary group of finite exponent when $k$ is imperfect of characteristic $p$.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.419/ |
| spellingShingle | Rosengarten, Zev Picard Groups of Algebraic Groups and an Affineness Criterion Comptes Rendus. Mathématique |
| title | Picard Groups of Algebraic Groups and an Affineness Criterion |
| title_full | Picard Groups of Algebraic Groups and an Affineness Criterion |
| title_fullStr | Picard Groups of Algebraic Groups and an Affineness Criterion |
| title_full_unstemmed | Picard Groups of Algebraic Groups and an Affineness Criterion |
| title_short | Picard Groups of Algebraic Groups and an Affineness Criterion |
| title_sort | picard groups of algebraic groups and an affineness criterion |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.419/ |
| work_keys_str_mv | AT rosengartenzev picardgroupsofalgebraicgroupsandanaffinenesscriterion |