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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.

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