the Homology of Completion and Torsion
Authors: Marco Porta, Liran Shaul and Amnon Yekutieli
Publication status: Algebras and Repesentation Theory 17 (2014), 31–67.
to: On the Homology of Completion and Torsion
Algebras and Representation Theory: Volume 18, Issue 5 (2015), Page 1401-1405
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.
published paper (full pdf requires permission)
updated 19 November 2015