On the Homology of Completion and Torsion

Marco Porta; Liran Shaul; Amnon Yekutieli

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arXiv · 1010.4386

On the Homology of Completion and Torsion

Marco Porta·Liran Shaul·Amnon Yekutieli

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Abstract

Let A be a commutative ring, and \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 \a-adically complete complexes and the category of cohomologically \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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BibTeX RIS

Marco Porta, Liran Shaul, Amnon Yekutieli. 2010-10-21. On the Homology of Completion and Torsion. https://arxiv.org/abs/1010.4386

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