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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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