An Isaac Newton Institute Programme

Model Theory and Applications to Algebra and Analysis

Groups definable in separably closed fields and algebraic groups: definable simplicity and "pseudo-simple" groups.

25th January 2005

Author: Elisabeth Bouscaren (CNRS - Paris 7)

Abstract

Many questions which we can answer in the case of superstable groups remain open for stable not superstable groups: existence of an infinite definable abelian subgorup, link between definable simplicity and simplicity for example. Separably closed fields are a good place to test all these questions. In the case of definably simple groups, one is led rapidly to interesting questions about the classification of pseudo-reductive algebraic groups over separably closed fields (in the terminology of Tits).