Jordan property for algebraic groups and automorphism groups of projective varieties in arbitrary characteristic

TL;DR

This paper extends Jordan's theorem to algebraic groups over fields of any characteristic, demonstrating a similar property for automorphism groups of projective varieties, thus broadening the understanding of group actions in algebraic geometry.

Contribution

It introduces a Jordan-type property for automorphism groups of projective varieties over arbitrary characteristic fields, generalizing previous results.

Findings

Jordan's theorem analogue for algebraic groups in any characteristic

Jordan-type property established for automorphism groups of projective varieties

Broadens applicability of Jordan's property in algebraic geometry

Abstract

We show an analogue of Jordan's theorem for algebraic groups defined over a field $\mathbb k$ of arbitrary characteristic. As a consequence, a Jordan-type property holds for the automorphism group of any projective variety over $\mathbb k$.