A remark on Rickard complexes

In this paper, we characterize a Rickard complex, which induces a Rickard equivalence between the block algebras of a block b and its Brauer correspondent and whose vertices have the same order as defect groups of the block b. The homology of such a Rickard complex vanishes at all degree but degree q, and the homology at degree q induces a basic Morita equivalence between the block algebras in the sense of Puig.