Notes from a problem session on support varieties

For groups other than p-groups, some work has been done for general situations [12, 13] and for simple groups [4, 5, 6]. Balmer [2] has made connections with the Picard group of the spectrum of the stable category. Nakano and the author have had some success extending the results to more general finite group schemes. For example, in the case of a p-restricted Lie algebra whose cohomology ring satisfies some mild conditions on dimension, it can be shown that the group of endotrivial modules is isomorphic to Z and generated by the class of Ω(k). It is interesting to note that one of the open problems in this case is whether the group of endotrivial modules is finitely generated. That is, for general group schemes it is not know if an indecomposable torsion endotrivial module must have bounded dimension as was true and essential in the above step 3 for finite groups.