On the arithmetic of pseudo-reductive and wound unipotent groups

Let k be a global function field. It is a well-known fact that
the first cohomology set of a reductive group over k has an abelian group
structure. In this talk we will show that the first cohomology set of an
arbitrary pseudo-reductive group over k can be naturally embedded in an
abelian group. Under a certain condition, the set in question has a natural
abelian group structure. We will also discuss class groups of wound
unipotent groups of toric type.