  Let A be a commutative ring, and let \a be a weakly proregular ideal in A.
(If A is noetherian then any ideal in it is weakly proregular.) Suppose M is a
compact generator of the category of cohomologically \a-torsion complexes. We
prove that the derived double centralizer of M is isomorphic to the \a-adic
completion of A. The proof relies on the MGM equivalence from [PSY] and on
derived Morita equivalence. Our result extends earlier work of
Dwyer-Greenlees-Iyengar [DGI] and Efimov [Ef].
