Comptes Rendus
Algebraic geometry
On homogeneous spaces with finite anti-solvable stabilizers
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 n6 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.

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
     author = {Giancarlo Lucchini Arteche},
     title = {On homogeneous spaces with finite anti-solvable stabilizers},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {777--780},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {360},
     year = {2022},
     doi = {10.5802/crmath.339},
     language = {en},
AU  - Giancarlo Lucchini Arteche
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PB  - Académie des sciences, Paris
DO  - 10.5802/crmath.339
LA  - en
ID  - CRMATH_2022__360_G7_777_0
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%A Giancarlo Lucchini Arteche
%T On homogeneous spaces with finite anti-solvable stabilizers
%J Comptes Rendus. Mathématique
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%I Académie des sciences, Paris
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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.

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