Classification of pseudo-reductive groups and its consequences

Mardi 5 mai 2009 16:00-17:00 - Prasad Gopal - Université du Michigan

Résumé : A connected algebraic group G defined over a field k is said to be pseudo-reductive if its unipotent radical does not contain any nontrivial connected subgroups defined over k. Such groups arise naturally. For example, any connected algebraic k-group G contains a unique maximal connected normal unipotent k-subgroup U ; the quotient G/U is a pseudo-reductive group. Classification of pseudo-reductive groups over arbitrary fields k is therefore an interesting problem. In a joint work with Brian Conrad (Stanford University) and Ofer Gabber (IHES) we have obtained a classification of such groups over any field of odd characteristic, and also over local and global function fields of characteristic 2. I will outline this classification. The classification has several interesting applications which will also be described in my talk.

Lieu : bât. 425 - 113-115

Classification of pseudo-reductive groups and its consequences  Version PDF