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Regular version of the site

Working paper

Automorphisms of pointless surfaces

For a geometrically rational surface X over a perfect field of characteristic different from 2 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 an auxiliary result, we show boundedness of finite subgroups in anisotropic linear algebraic groups of bounded rank and number of connected components. Also, we provide applications to Jordan property for groups of birational automorphisms.