Sheaves and local equivalence relations
We start with a small paradigm shift about group representations, namely the observation that restriction to a subgroup can be understood as an extension-of-scalars. We deduce that, given a group , the derived and the stable categories of representations of a subgroup can be constructed out of the corresponding category for by a purely triangulated-categorical construction, analogous to étale extension in algebraic geometry. In the case of finite groups, we then use descent methods to investigate...