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arXiv · 1207.0612

Completion by Derived Double Centralizer

Marco Porta·Liran Shaul·Amnon Yekutieli
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Abstract

Let A be a commutative ring, and let \a be a weakly proregular ideal in A. (If A is noetherian then any ideal in it is weakly proregular.) Suppose M is a compact generator of the category of cohomologically \a-torsion complexes. We prove that the derived double centralizer of M is isomorphic to the \a-adic completion of A. The proof relies on the MGM equivalence from [PSY] and on derived Morita equivalence. Our result extends earlier work of Dwyer-Greenlees-Iyengar [DGI] and Efimov [Ef].

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BibTeXRIS

Marco Porta, Liran Shaul, Amnon Yekutieli. 2013-01-21. Completion by Derived Double Centralizer. https://arxiv.org/abs/1207.0612

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