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Finite groups acting on Severi–Brauer surfaces

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We classify finite groups that can act by automorphisms and birational automorphisms on non-trivial Severi–Brauer surfaces over fields of characteristic zero.

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Acknowledgements

I am grateful to Sergei Gorchinskiy, Leonid Rybnikov, Andrey Trepalin, and Vadim Vologodsky for useful discussions. I am also grateful to the referee for helpful comments, and especially for Remark 7.2. Special thanks go to Denis Osipov who spotted a gap in a preliminary version of the paper and suggested several improvements of the exposition.

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Authors and Affiliations

  1. Steklov Mathematical Institute of Russian Academy of Sciences, 8 Gubkina Str., Moscow, Russia, 119991

    Constantin Shramov

  2. National Research University Higher School of Economics, Laboratory of Algebraic Geometry, 6 Usacheva Str., Moscow, Russia, 119048

    Constantin Shramov

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  1. Constantin Shramov
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Correspondence to Constantin Shramov.

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The author was partially supported by the HSE University Basic Research Program, Russian Academic Excellence Project “5-100”, and by the Foundation for the Advancement of Theoretical Physics and Mathematics “BASIS”.

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Shramov, C. Finite groups acting on Severi–Brauer surfaces. European Journal of Mathematics 7, 591–612 (2021). https://doi.org/10.1007/s40879-020-00448-3

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  • DOI: https://doi.org/10.1007/s40879-020-00448-3

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