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Algebraic geometry
On homogeneous spaces with finite anti-solvable stabilizers
Giancarlo Lucchini Arteche1
1 Departamento de Matemáticas, Facultad de Ciencias, Universidad de Chile, Las Palmeras 3425, Ñuñoa, Santiago, Chile
Comptes Rendus. Mathématique, Volume 360 (2022), pp. 777-780.

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≠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=SL n , all such homogeneous spaces have rational points.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/crmath.339
Classification: 14M17, 12G05, 14G05
Keywords: homogeneous spaces, rational points, non-abelian cohomology, finite simple groups

Giancarlo Lucchini Arteche 1

1 Departamento de Matemáticas, Facultad de Ciencias, Universidad de Chile, Las Palmeras 3425, Ñuñoa, Santiago, Chile
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Giancarlo Lucchini Arteche. On homogeneous spaces with finite anti-solvable stabilizers. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 777-780. doi : 10.5802/crmath.339. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.339/

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