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Automorphisms of surfaces over fields of positive characteristic

Yifei Chen and Constantin Shramov

Geometry & Topology 28 (2024) 2747–2791
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 nonnegative Kodaira dimension is Jordan in the usual sense.

Keywords
birational automorphism group, $p$–Jordan property
Mathematical Subject Classification
Primary: 14E07, 14J50
References
Publication
Received: 23 July 2021
Revised: 25 October 2022
Accepted: 17 December 2022
Published: 21 October 2024
Proposed: Dan Abramovich
Seconded: Mark Gross, Yakov Eliashberg
Authors
Yifei Chen
Hua Loo-Keng Key Laboratory of Mathematics
Academy of Mathematics and Systems Science
Chinese Academy of Sciences
Beijing
China
Constantin Shramov
Steklov Mathematical Institute of Russian Academy of Sciences
Moscow
Russia
Laboratory of Algebraic Geometry
National Research University Higher School of Economics
Moscow
Russia

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