Tuesday, July 19.7., 14:00
Martin Gallauer (MPIM Bonn)
The derived category of permutation modules.
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.