Foxby equivalence, complete modules, and torsion modules
An equivalence theory for derived categories over differential graded algebras is developed using the adjoint functors and the classes of objects for which the values of unit and counit of adjunction are isomorphisms (Auslander and Bass classes). Some properties of the new equivalence are shown. It is proved that both classical Foxby equivalence (for Noetherian, local, commutative rings) and the Morita equivalence for complete modules and torsion modules, developed by Dwyer and Greenless, arise as special cases. Moreover, a new instance of this theory (Matlis equivalence) gives a characterization of Gorenstein rings.
scientific article; zbMATH DE number 1839052