Pol, Luca and Williamson, Jordan (2022) The homotopy theory of complete modules. JOURNAL OF ALGEBRA, 594. pp. 74-100. ISSN 0021-8693, 1090-266X
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Given a commutative ring R and finitely generated ideal I, one can consider the classes of I-adically complete, L-0(I)-complete and derived I -complete complexes. Under a mild assumption on the ideal I called weak pro-regularity, these three notions of completions interact well. We consider the classes of I-adically complete, L-0(I)-complete and derived I -complete complexes and prove that they present the same homotopy theory. Given a ring homomorphism R -> S, we then give necessary and sufficient conditions for the categories of complete R complexes and the categories of complete S -complexes to have equivalent homotopy theories. This recovers and generalizes a result of Sather-Wagstaff and Wicklein on extended local (co)homology. (c) 2021 Elsevier Inc. All rights reserved.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | LOCAL COHOMOLOGY; HOMOLOGY; Completion; Homotopical algebra; Local homology |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 29 Jan 2024 13:49 |
| Last Modified: | 29 Jan 2024 13:49 |
| URI: | https://pred.uni-regensburg.de/id/eprint/57809 |
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