Title:       Cohomology with Grosshans graded coefficients, version II
Author:      Wilberd van der Kallen
Institution: Universiteit Utrecht
Home Page:   http://www.math.uu.nl/people/vdkallen/kallen.html
Status:      Preprint

Abstract:  Let the reductive group $G$ act on the finitely generated
commutative $k$-algebra $A$. We ask if the finite generation property
of the ring of invariants extends to the full cohomology ring.
In the previous version we confirmed this when the action on $A$ 
is replaced by the `contracted' action on the Grosshans graded ring
$\gr A$, provided the characteristic of $k$ is large.
In the present version we settle the case $G=SL_2$. 
We pose several questions, whose solution would
have significance for the main problem.