Title: On the Homology of Completion and Torsion
Authors: Marco Porta, Liran Shaul and Amnon Yekutieli
Publication status: Eprint arxiv:1010.4386 at http://arxiv.org

Abstract:
Let A be a noetherian commutative ring, and \a an ideal in it. In this
paper we study several properties of the derived \a-adic completion
functor and the derived \a-torsion functor. The first half of the
paper is devoted to a new proof of the GM Duality (first proved by
Alonso, Jeremias and Lipman). We also prove the closely related 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 D(Mod A).

In the second half of the paper we prove a few new results:
(1) A characterization of the category of cohomologically \a-adically
complete complexes as the right perpendicular to the derived localization
of A at \a; this is a generalization of a result of Kashiwara and
Schapira. (2) The Cohomologically Complete Nakayama Theorem. (3) A
characterization of cohomologically cofinite complexes. (4) A theorem
on completion by derived double centralizer, which is related to recent
work of Efimov.

Electronic Preprint:

• paper (pdf, 59 pages)

updated 26 Feb 2011