Complete modules and torsion modules (Q2784133)
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scientific article; zbMATH DE number 1731127
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Complete modules and torsion modules |
scientific article; zbMATH DE number 1731127 |
Statements
Complete modules and torsion modules (English)
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22 May 2003
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derived category of differential graded modules
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torsion objects
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complete objects
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Morita theory
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Bousfield localization
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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. NEWLINENEWLINENEWLINEThe authors develop a Morita theory for these subcategories and show that the Bousfield localization [\textit{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.
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