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arXiv · 2105.12242

On homogeneous spaces with finite anti-solvable stabilizers

Giancarlo Lucchini Arteche
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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 $n\neq 6$ 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.

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Giancarlo Lucchini Arteche. 2021-05-25. On homogeneous spaces with finite anti-solvable stabilizers. https://doi.org/10.5802/crmath.339

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