On the homology of completion and torsion Academic Article uri icon


  • Let A be a commutative ring, and \({\mathfrak{a}}\) 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 \({\mathfrak{a}}\) -adically complete complexes and the category of cohomologically \({\mathfrak{a}}\) -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.

publication date

  • January 1, 2014