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Complete modules and torsion modules. (English) Zbl 1017.18008
Let $$A$$ be a chain complex over a ring $$R$$. Inside the derived category of differential graded $$R$$-modules subcategories of $$A$$-torsion and $$A$$-complete objects can be defined naturally.
The authors develop a Morita theory for these subcategories and show that the Bousfield localization [A. K. Bousfield, Topology 14, 133-150 (1975; Zbl 0309.55013)] appears as one of the associated functors. In appropriate commutative situations those associated functors are identified as local homology and local cohomology.

##### MSC:
 18E30 Derived categories, triangulated categories (MSC2010) 55P60 Localization and completion in homotopy theory
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