On homogeneous spaces with finite anti-solvable stabilizers

Abstract

We say that a group is anti-solvable if all of its composition factors are non-abelian. We consider a particular family of anti-solvable finite groups containing the simple alternating groups for $n\ne 6$ and all 26 sporadic simple groups. We prove that, if $K$ is a perfect field and $X$ is a homogeneous space of a smooth algebraic $K$-group $G$ with finite geometric stabilizers lying in this family, then $X$ is dominated by a $G$-torsor. In particular, if $G={\mathrm{SL}}_n$, all such homogeneous spaces have rational points.

3 pages. Comments welcome :D

Cited by in corpus (1)

• Supersolvable descent for rational points