Séminaires : Séminaire Claude Chevalley

Equipe(s) :
Responsables :O. Brunat, M. Cabanes, et O. Dudas.
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Salle : 11 rue Pierre et Marie Curie - 75005 Paris
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Description

Orateur(s) Sebastian HERPEL - Bochum,
Titre On the smoothness of centralizers in reductive groups
Date16/02/2012
Horaire10:30 à 11:30
Diffusion
RésumeLet $G$ be a connected reductive algebraic group over an algebraically closed field. The question whether the scheme-theoretic centralizer of a closed subgroup of $G$ is smooth, or equivalently whether the dimensions of the global and infinitesimal centralizers coincide, occurs naturally in many contexts. We introduce a condition for the characteristic of the ground field that is slightly weaker than the notion of ``very good'' characteristic. We go on to show that this condition is necessary and sufficient for the smoothness of all centralizers of closed subgroup schemes. Reductive groups defined in such ``pretty good'' characteristic are closely related to so called standard groups, for instance to groups satisfying the standard hypotheses of Jantzen.
Salle11 rue Pierre et Marie Curie - 75005 Paris
Adresse
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