### abstract

- Let K be a commutative ring, and let A and B be associative unital K-algebras. We denote by Mod A and ModB the corresponding categories of left modules. One says that A and B are Morita equivalent relative to K (in the classical sense) if there is a K-linear equivalence of categories Mod A → ModB. Let Db(ModA) denote the bounded derived category of complexes of left A- modules. This is a K-linear triangulated category. If there is a K-linear equivalence of triangulated categories Db(ModA) → Db(ModB), then one says that A and B are derived Morita equivalent relative to K. There are plenty of examples of pairs of algebras that are derived Morita equiv- alent, but are not Morita equivalent in the classical sense. Now suppose K is a complete noetherian local ring, with maximal ideal m and residue field k. Let A be a flat m-adically complete K-algebra, such that the k- algebra ¯A := k ⊗ … Acknowledgments. The problem was …