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arXiv · 2107.14530

Quotients of Severi-Brauer surfaces

Andrey Trepalin
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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 $G \subset \operatorname{Aut}(S)$ is $\Bbbk$-rational, if and only if $|G|$ is divisible by $3$. Otherwise, the quotient is birationally equivalent to $S$.

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Andrey Trepalin. 2021-07-30. Quotients of Severi-Brauer surfaces. https://arxiv.org/abs/2107.14530

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