Orateur(s) | Sebastian HERPEL - Bochum,
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Titre | On the smoothness of centralizers in reductive groups |
Date | 16/02/2012 |
Horaire | 10:30 à 11:30 |
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Diffusion | |
Résume | Let $G$ 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. |
Salle | 11 rue Pierre et Marie Curie - 75005 Paris |
Adresse | |