Online Talk

This is joint work in progress with Martin Gallauer. Our aim is to give a proper definition of the "stable permutation category" in modular representation theory of finite groups, that is with coefficients in a field of positive characteristic p. That category is to the ordinary stable module category what the derived permutation category is to the ordinary derived category. Our construction is guided by tensor-triangular geometry and the picture obtained in our study of the geometry of permutation modules. This new stable permutation category is often connected, like the usual stable module category, but it can disconnect in special cases and we discuss when this happens and what the connected components are.