Sous-schémas en groupes unipotents normaux de groupes réductifs

Adrian Vasiu

doi:10.1016/j.crma.2005.05.014

Sous-schémas en groupes unipotents normaux de groupes réductifs

Translated title of the contribution: Normal, unipotent subgroup schemes of reductive groups

Adrian Vasiu

Mathematics and Statistics

Binghamton University

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

Let G be a reductive group over a field k of characteristic p. Let k^sep be a separable closure of k. If p ≠ 2, there exists a linear representation of G that is faithful and semisimple; moreover, any unipotent, normal subgroup scheme of G is trivial. For p = 2, these two properties hold if and only if G_ksep has no direct factor that is isomorphic to SO_2n+1 for some n ≥ 1.

Translated title of the contribution	Normal, unipotent subgroup schemes of reductive groups
Original language	French
Pages (from-to)	79-84
Number of pages	6
Journal	Comptes Rendus Mathematique
Volume	341
Issue number	2
DOIs	https://doi.org/10.1016/j.crma.2005.05.014
State	Published - Jul 15 2005

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abstract = "Let G be a reductive group over a field k of characteristic p. Let ksep be a separable closure of k. If p ≠ 2, there exists a linear representation of G that is faithful and semisimple; moreover, any unipotent, normal subgroup scheme of G is trivial. For p = 2, these two properties hold if and only if Gksep has no direct factor that is isomorphic to SO2n+1 for some n ≥ 1.",

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AB - Let G be a reductive group over a field k of characteristic p. Let ksep be a separable closure of k. If p ≠ 2, there exists a linear representation of G that is faithful and semisimple; moreover, any unipotent, normal subgroup scheme of G is trivial. For p = 2, these two properties hold if and only if Gksep has no direct factor that is isomorphic to SO2n+1 for some n ≥ 1.

UR - https://www.scopus.com/pages/publications/22644444563

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DO - 10.1016/j.crma.2005.05.014

M3 - Article

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JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

IS - 2

ER -

Sous-schémas en groupes unipotents normaux de groupes réductifs

Abstract

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