Boundedness for finite subgroups of linear algebraic groups

Boundedness for finite subgroups of linear algebraic groups

We show the boundedness of finite subgroups in any anisotropic reductive 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.

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Veröffentlicht in:Transactions of the American Mathematical Society 2021-12, Vol.374 (12), p.9029-9046
Hauptverfasser: Shramov, Constantin, Vologodsky, Vadim
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics
Physical Sciences
Science & Technology
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Zusammenfassung:We show the boundedness of finite subgroups in any anisotropic reductive 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.
ISSN:0002-9947
1088-6850
DOI:10.1090/tran/8511