We work in the group algebra kG of a finite group scheme defined over a field of characteristic p > 0. The stable category stmod(kG) of finitely generated kG-modules is tensor triangulated category of compact objects. Associated to any thick tensor ideal subcategory 𝒞 is a distinguished triangle → E → k → F → where E and F are idempotent modules in the stable category StMod(kG) of all kG-modules. Tensoring with F is the localization functor associated to 𝒞. Indeed, the endomorphism ring of F is the endomorphism ring of the trivial module in the localized category. In this lecture, we will discuss some results on the nature of the endomorphism ring of the module F and some strange variant support varieties for modules.
This video is part of the New Directions in Group Theory and Triangulated Categories seminar series.
