Orateur(s)  Sebastian HERPEL  Bochum,

Titre  On the smoothness of centralizers in reductive groups 
Date  16/02/2012 
Horaire  10:30 à 11:30 

Diffusion  
Résume  Let $G$ be a connected reductive algebraic group over an algebraically closed field. The question whether the schemetheoretic 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. 
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