Title:
Completion by Derived
Double Centralizer
Authors:
Marco Porta, Liran Shaul and Amnon Yekutieli
Publication status:
Algebras
and Representation Theory
17
(2014)
481-494.
Abstract:
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].
published paper (full pdf requires permission)
updated 27 March 2014