Title:       A reductive group with finitely generated cohomology algebras
Author:      Wilberd van der Kallen
Institution: Universiteit Utrecht
Home Page:   http://www.math.uu.nl/people/vdkallen/kallen.html
Status:      Preprint

Abstract:  Let $G$ be the linear algebraic group $\SL_3$ over a field $k$ of
characteristic two.
Let $A$ be a finitely generated commutative $k$-algebra on which $G$ acts
rationally by $k$-algebra automorphisms.
We show that the full cohomology ring $H^*(G,A)$ is finitely generated.
This extends the finite generation property of the ring of invariants
$A^G$. We discuss where the problem stands for other
geometrically reductive group schemes.