Comptes Rendus
Algebraic geometry
Picard Groups of Algebraic Groups and an Affineness Criterion
Comptes Rendus. Mathématique, Volume 361 (2023), pp. 559-564.

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.

Nous prouvons qu’un groupe algébrique sur un corps k est affine si et seulement si son groupe de Picard est de torsion, et que dans ce cas, le groupe de Picard est fini si k est parfait, et le produit d’un groupe fini d’ordre premier à p par un p-groupe d’exposant fini lorsque k est imparfait de caractéristique p.

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DOI: 10.5802/crmath.419
Classification: 14L10, 14L15, 14L17, 14L40, 20G15

Zev Rosengarten 1

1 Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Edmond J. Safra Campus, 91904, Jerusalem, Israel
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Zev Rosengarten. Picard Groups of Algebraic Groups and an Affineness Criterion. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 559-564. doi : 10.5802/crmath.419. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.419/

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[8] Zev Rosengarten Tate Duality In Positive Dimension Over Function Fields (2021) (https://arxiv.org/abs/1805.00522, to appear in Memoirs of the American Mathematical Society)

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