Perverse equivalences and Brouéʼs conjecture

We give a new approach to the construction of derived equivalences between blocks of finite groups, based on perverse equivalences, in the setting of Brouéʼs abelian defect group conjecture. We provide in particular local and global perversity data describing the principal blocks and the derived equivalences for a number of finite simple groups with Sylow subgroups elementary abelian of order 9. We also examine extensions to automorphism groups in a general setting.