Dualizing Complexes, Morita Equivalence and the Derived Picard Group of a Ring

Two rings A and B are said to be derived Morita equivalent if the derived categories Db(Mod A) and Db(Mod B) are equivalent. If A and B are derived Morita equivalent algebras over a field k, then there is a complex of bimodules T such that the functor T⊗LA−:Db(Mod A) → Db(Mod B) is an equivalence. The complex T is called a tilting complex.