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arXiv · 2205.04959

Picard Groups Of Algebraic Groups And An Affineness Criterion

Zev Rosengarten
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Abstract

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 $p$.

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Zev Rosengarten. 2022-05-10. Picard Groups Of Algebraic Groups And An Affineness Criterion. https://arxiv.org/abs/2205.04959

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