Achim Krause (UiO): Picard groups of stable module categories

Abstract: For a group G and commutative ring R, the stable module category of G
with R-coefficients is obtained roughly by considering "R[G]-modules
up to projective R[G]-modules".  Invertible objects in this category
(called "endotrivial modules") show up in representation theory and have
been studied extensively in the case of R a field of characteristic p.
In joint work with Jesper Grodal, we aim to understand what happens
for other rings, particularly the integers.  We prove that this case is
controlled by some interesting character-theoretic obstruction.