Completion by Derived Double Centralizer
Commutative Algebra
2013-01-22 v2 Algebraic Geometry
Category Theory
K-Theory and Homology
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].
Cite
@article{arxiv.1207.0612,
title = {Completion by Derived Double Centralizer},
author = {Marco Porta and Liran Shaul and Amnon Yekutieli},
journal= {arXiv preprint arXiv:1207.0612},
year = {2013}
}
Comments
13 pages; minor changes; final version, to appear in Algebr. Represent. Theor