Splendid and perverse equivalences
Journal of Algebra(2016)
摘要
Inspired by the works of Rickard on splendid equivalences [9] and of Chuang and Rouquier on perverse equivalences [6], we are here interested in the combination of both, i.e. 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 groups.
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关键词
Representation theory of finite groups,Derived equivalences,Splendid equivalences,Perverse equivalences
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