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arXiv · 2106.15906

Automorphisms of surfaces over fields of positive characteristic

Yifei Chen·Constantin Shramov
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Abstract

We study automorphism and birational automorphism groups of varieties over fields of positive characteristic from the point of view of Jordan and $p$-Jordan property. In particular, we show that the Cremona group of rank $2$ over a field of characteristic $p>0$ is $p$-Jordan, and the birational automorphism group of an arbitrary geometrically irreducible algebraic surface is nilpotently $p$-Jordan of class at most $2$. Also, we show that the automorphism group of a smooth geometrically irreducible projective variety of non-negative Kodaira dimension is Jordan in the usual sense.

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Yifei Chen, Constantin Shramov. 2021-06-30. Automorphisms of surfaces over fields of positive characteristic. https://doi.org/10.2140/gt.2024.28.2747

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