Work

Birational Automorphism Groups of Severi–Brauer Surfaces Over the Field of Rational Numbers

Year: 2024

Type: article

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 $\textrm{Bir}(V)$ 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 $\textrm{Bir}(V)$ 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.

Source: International Mathematics Research Notices

DOI: 10.1093/imrn/rnae249

Author: Anastasia V Vikulova

Institutions: Russian Academy of Sciences, Steklov Mathematical Institute

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Basis Foundation, Ministry of Science and Higher Education of the Russian Federation

Awards: G597338630, G6444257319, G6509858906