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arXiv · 2605.25788

Jordan property of birational automorphism groups of surfaces and birational permutations

Alexandr Zaitsev
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Abstract

We prove that the group of birational automorphisms of a geometrically irreducible algebraic surface over a finite field is Jordan. We show that the analogous statement fails in higher dimensions. Finally, we prove that groups of birational permutations over finite fields have bounded finite $p'$-subgroups; in particular, they are $p$-Jordan.

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Alexandr Zaitsev. 2026-05-25. Jordan property of birational automorphism groups of surfaces and birational permutations. https://arxiv.org/abs/2605.25788

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