Algebra Seminar: Pauwels -- The etale site of the stable module category of a finite group

Bregje Pauwels (ANU) 

Friday 23 March, 12-1pm, Place: Carslaw 375 

Title: The etale site of the stable module category of a finite group 

Abstract: To any tensor-triangulated category T, there is a natural way to associate a
site and a sheaf cohomology.  The objects in this site are the commutative separable
monoids in T.  For instance, if T is the derived category of quasi-coherent sheaves on a
scheme X, then the site fits in between the classical etale site and the recently
discovered pro-etale site on X.  

In this talk, I will explain what separable monoids are and show how they pop up in
various settings.  For a finite group G, I will show that the compact separable monoids
in both the derived and stable module category of G correspond to G-sets.  This allows
us to describe the site associated to the derived and stable module category of G, to
compute the corresponding sheaf cohomology and its relation to traditional group
cohomology.