Picard Groups Of Algebraic Groups And An Affineness Criterion

2022/05/10 by Rosengarten, Zev
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2205.04959

Abstract

We prove that an algebraic group over a field kis 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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