Unipotent elements in small characteristic

Abstract

We make a study of unipotent elements in a connected reductive group over an algebraically closed field with emphasis on the case where the characteristic is a bad prime. We try to see how much of the theory of Dynkin-Kostant extends to this case. We also study the variety of Borel subgroups containing a unipotent element and prove a purity property for its cohomology in certain cases in bad characteristic.