Completion by Derived
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].
updated 27 March 2014