Abstract—We show that a quotient of a non-trivial Severi–Brauer surface S over arbitrary field \(\Bbbk \) of characteristic 0 by a finite group \(G \subset {\text{Aut}}(S)\) is \(\Bbbk \)-rational if and only if |G| is divisible by 3. Otherwise, the quotient is birationally equivalent to S.
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ACKNOWLEDGMENTS
The author is grateful to Costya Shramov and Sergey Gorchinskiy for many useful discussions and comments.
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The study has been funded within the framework of the HSE University Basic Research Program.
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Trepalin, A.S. Quotients of Severi–Brauer Surfaces. Dokl. Math. 104, 390–393 (2021). https://doi.org/10.1134/S106456242106017X
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DOI: https://doi.org/10.1134/S106456242106017X