  Inspired by the works of Rickard on splendid equivalences and of Chuang and
Rouquier on perverse equivalences, we are here interested in the combination of
both, a splendid perverse equivalence. This is naturally the right framework to
understand the relations between global and local perverse equivalences between
blocks of finite groups, as a splendid equivalence induces local derived
equivalences via the Brauer functor. We prove that under certain conditions, we
have an equivalence between a perverse equivalence between the homotopy
category of p-permutation modules and local derived perverse equivalences, in
the case of abelian defect group.

Representation Theory