The category of strict polynomial functors, introduced by Friedlander and Suslin in 1997, has played an important role over the years in establishing various finite-generation results for the cohomology of finite group schemes. In 2013, Axtell introduced the corresponding category of strict polynomial superfunctors. In this talk, I’ll describe how Ext-group calculations in the category of strict polynomial superfunctors have led to our current (though still incomplete) picture of the cohomology of finite supergroup schemes and restricted Lie superalgebras. I’ll also touch on some of the directions in which progress in better understanding the superfunctor category is waiting to be made.
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