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arXiv · 1406.2123

Splendid and perverse equivalences

Léo Dreyfus-Schmidt
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Abstract

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.

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Léo Dreyfus-Schmidt. 2014-06-09. Splendid and perverse equivalences. https://arxiv.org/abs/1406.2123

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