Support varieties and Hochschild cohomology rings
Nicole Snashall and 0yvind Solberg

Abstract.
We define a support variety for finitely generated modules over any artin
algebra $\Lambda$ in terms of the maximal ideal spectrum of the algebra
$\HH^*(\Lambda)$ of $\Lambda$. This is modelled on what is done in modular
representation theory, and the varieties defined in this way are shown to have
many of the same properties as for group rings. In fact the notion of a variety
in our sense and for principal and non-principal blocks are related by a finite
surjective map of varieties. For a selfinjective artin algebra the variety is
shown to be an invariant of the stable component of the Auslander-Reiten 
quiver. Moreover we give information on nilpotent elements in $\HH^*(\Lambda)$,
give a thorough discussion of the ring $\HH^*(\Lambda)$ on a class of 
Nakayama algebras, a brief discussion on a possible notion of complexity and 
make a comparison with support varieties for complete intersections.