Birational automorphism groups of Severi-Brauer surfaces over the field of rational numbers

Abstract

We prove that the only non-trivial finite subgroups of birational automorphism group of non-trivial Severi--Brauer surfaces over the field of rational numbers are~$\mathbb{Z}/3\mathbb{Z}$ and $(\mathbb{Z}/3\mathbb{Z}{)}^2.$ Moreover, we show that $(\mathbb{Z}/3\mathbb{Z}{)}^2$ is contained in $\mathrm{Bir}(V)$ for any Severi--Brauer surface $V$ over a field of characteristic different from $2$ and $3$, and $(\mathbb{Z}/3\mathbb{Z}{)}^3$ is contained in $\mathrm{Bir}(V)$ for any Severi--Brauer surface~$V$ over a field of characteristic different from $2$ and $3$ which contains a non-trivial cube root of unity.

References in corpus (1)

• Automorphisms of surfaces over fields of positive characteristic

Cited by in corpus (1)

• Automorphisms of del Pezzo surfaces without points