Martin Gallauer (MPIM Bonn)

The derived category of permutation modules.

Abstract:

To a field k and a finite group G one associates the derived category of kG-modules, an important invariant that is difficult to understand in general. At least, viewed through the lens of tensor-triangular geometry, it admits a familiar description in terms of the support variety. We propose to study a refinement, the derived category of G-permutation modules over k. It has interesting interpretations in algebraic geometry, representation theory and equivariant homotopy theory. We will explain what we know about its tensor-triangular geometry. This is based on joint work, mostly in progress, with Paul Balmer.