On the homology of completion and torsion

Marco Porta, Liran Shaul, Amnon Yekutieli

Research output: Contribution to journalArticlepeer-review

57 Scopus citations

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.

Original languageEnglish
Pages (from-to)31-67
Number of pages37
JournalAlgebras and Representation Theory
Volume17
Issue number1
DOIs
StatePublished - 1 Feb 2014

Keywords

  • Adic completion
  • derived functors
  • torsion

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