On the Homology of Completion and Torsion
Commutative Algebra
2012-10-17 v5 Algebraic Geometry
K-Theory and Homology
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.
Keywords
Cite
@article{arxiv.1010.4386,
title = {On the Homology of Completion and Torsion},
author = {Marco Porta and Liran Shaul and Amnon Yekutieli},
journal= {arXiv preprint arXiv:1010.4386},
year = {2012}
}
Comments
This version: 33 pages. Final version, to appear in Algebras and Representation Theory. Minor changes in text