Automorphisms of pointless surfaces

2018/07/17 by Shramov, Constantin, Vologodsky, Vadim · 1 citation
#14E07 #14J26 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1807.06477

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.

Cited by

• The Degree of Irrationality of del Pezzo Surfaces

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