Boundedness for finite subgroups of linear algebraic groups

TL;DR

This paper proves the boundedness of finite subgroups in certain algebraic groups over perfect fields containing all roots of unity, and provides explicit bounds for automorphism groups of specific algebraic varieties.

Contribution

It establishes boundedness results for finite subgroups in anisotropic reductive algebraic groups and gives explicit bounds for automorphism groups of Severi-Brauer varieties and quadrics.

Findings

Finite subgroups are bounded in anisotropic reductive algebraic groups over specified fields.

Explicit bounds are provided for automorphism groups of Severi-Brauer varieties.

Results apply to fields containing all roots of unity.

Abstract

We show the boundedness of finite subgroups in any anisotropic reductive algebraic group over a perfect field that contains all roots of 1. Also, we provide explicit bounds for orders of finite subgroups of automorphism groups of Severi-Brauer varieties and quadrics over such fields.