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We give a self-contained account of an alternative proof of J. Rickard's Morita-theorem for derived categories [135] and his theorem on the realization of derived equivalences as derived functors [139]. To this end, we first review the basic facts on unbounded derived categories (complexes unbounded to the right and to the left) and on derived functors between such categories (cf. [159], [19]). We...
The aim of the present text is to report on some properties of stable equivalences of Morita type and derived equivalences. In the first section we describe, very roughly, a panorama of various types of equivalences between blocks of group algebras, in order to give an idea of the context of what we are going to do in the sequel. In section 2 we recall from [110] the basic properties of Broué's notion...
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