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Derived equivalences and stable equivalences of Morita type

Derived equivalences and stable equivalences of Morita type are two foundamental equivalences for finite dimensional algebras. For self-injective algebras, Rickard proved that a derived equivalence always induces a stable equivalence of Morita type. In a joint work with C.C.Xi, the notion of almost $\nu$-stable derived equivalence for general finite dimensional algebras was introduced, which generalizes the above mentioned result of Rickard. In this talk, We shall discuss the other direction, namely, how one can get a derived equivalence from a given stable equivalence of Morita type.