Abstract
Let A be a commutative ring, and \({\mathfrak{a}}\) a weakly proregular ideal in A. This includes the noetherian case: if A is noetherian then any ideal in it is weakly proregular; but there are other interesting examples. In this paper we prove the MGM equivalence, which is an equivalence between the category of cohomologically \({\mathfrak{a}}\) -adically complete complexes and the category of cohomologically \({\mathfrak{a}}\) -torsion complexes. These are triangulated subcategories of the derived category of A-modules. Our work extends earlier work by Alonso–Jeremias–Lipman, Schenzel and Dwyer–Greenlees.
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This research was supported by the Israel Science Foundation and the Center for Advanced Studies at BGU.
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Porta, M., Shaul, L. & Yekutieli, A. On the Homology of Completion and Torsion. Algebr Represent Theor 17, 31–67 (2014). https://doi.org/10.1007/s10468-012-9385-8
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DOI: https://doi.org/10.1007/s10468-012-9385-8