  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.
