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arXiv · 1807.06477

Automorphisms of pointless surfaces

Constantin Shramov·Vadim Vologodsky
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Abstract

For a geometrically rational surface X over an arbitrary field of characteristic different from 2 and 3 that contains all roots of 1, we show that either X is birational to a product of a projective line and a conic, or the group of birational automorphisms of X has bounded finite subgroups. As a key step in the proof, we show boundedness of finite subgroups in any anisotropic reductive algebraic group over a perfect field that contains all roots of 1. Also, we provide applications to Jordan property for groups of birational automorphisms.

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Constantin Shramov, Vadim Vologodsky. 2018-07-17. Automorphisms of pointless surfaces. https://arxiv.org/abs/1807.06477

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