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Mathematics > Algebraic Geometry

arXiv:1807.06477 (math)
[Submitted on 17 Jul 2018 (v1), last revised 14 Aug 2020 (this version, v4)]

Title:Automorphisms of pointless surfaces

Authors: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.
Comments: Minor corrections; 46 pages
Subjects: Algebraic Geometry (math.AG)
MSC classes: 14E07, 14J26
Cite as: arXiv:1807.06477 [math.AG]
  (or arXiv:1807.06477v4 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1807.06477

Submission history

From: Constantin Shramov [view email]
[v1] Tue, 17 Jul 2018 14:47:20 UTC (38 KB)
[v2] Wed, 8 May 2019 16:48:21 UTC (46 KB)
[v3] Mon, 27 Jan 2020 15:45:02 UTC (49 KB)
[v4] Fri, 14 Aug 2020 19:30:50 UTC (49 KB)
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