Quotients of Severi–Brauer Surfaces

A. S. Trepalin^a^,^b^,*

^aSteklov Mathematical Institute of Russian Academy of Sciences, Moscow, 119991 Russia

^bLaboratory of Algebraic Geometry, National Research University Higher School of Economics, Moscow, 119048 Russia

Correspondence to: *e-mail: trepalin@mccme.ru

Received 5 August, 2021

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.

Keywords: Severi–Brauer surfaces, rationality problems, Brauer group, minimal model program

DOI: 10.1134/S106456242106017X