Abstract

Since the remarkable discovery of the relevance of derived equivalences in the theory of p-blocks of finite groups, where p is a prime, by J. Rickard in [15, 16], various attempts have been made to understand this phenomenon. In particular, J. Rickard defines in [18] a certain class of derived equivalences between the derived module categories of p-blocks of finite groups that he calls splendid equivalences (and that we are going to call splendid derived equivalences in this paper) which take into account the local structure, that is, which under suitable hypotheses induce a family of derived equivalences at all ‘local levels’ of the considered p-blocks (see [18] for a more detailed motivation). The main condition for a derived equivalence to be splendid is that it is given by a two-sided tilting complex consisting of p-permutation bimodules (see Definitions 1.3 and 1.4 below for the precise terminology).

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