Quotients of Severi-Brauer surfaces

Abstract

We show that a quotient of a non-trivial Severi-Brauer surface $S$ over arbitrary field $\mathbb{k}$ of characteristic $0$ by a finite group $G\subset \mathrm{Aut}(S)$ is $\mathbb{k}$-rational, if and only if $|G|$ is divisible by $3$. Otherwise, the quotient is birationally equivalent to $S$.

6 pages