# Séminaires : Séminaire d'Algèbre

 Equipe(s) : gr, Responsables : J. Alev, D. Hernandez, B. Keller, Th. Levasseur, et S. Morier-Genoud. Email des responsables : Jacques Alev , David Hernandez , Bernhard Keller , Thierry Levasseur , Sophie Morier-Genoud Salle : 001 Adresse : IHP Description

 Orateur(s) Amnon YEKUTIELI - Ben Gurion University, Israel et Université Paris 7, Titre Cohomologically complete complexes Date 24/10/2011 Horaire 14:30 à 15:30 Résume Let $A$ be a noetherian commutative ring, and $\mathfrak{a}$ an ideal in it. In this lecture I will talk about several properties of the derived $\mathfrak{a}$-adic completion functor and the derived $\mathfrak{a}$-torsion functor. In the first half of the talk I will discuss $\mathfrak{a}$-adically projective modules, GM Duality (first proved by Alonso, Jeremias and Lipman), and the closely related MGM Equivalence. The latter 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 D(Mod $A$). In the second half of the talk I will discuss new results: (1) A characterization of the category of cohomologically $\mathfrak{a}$-adically complete complexes as the right perpendicular to the derived localization of $A$ at $\mathfrak{a}$. This shows that our definition of cohomologically $\mathfrak{a}$-adically complete complexes coincides with the original definition of Kashiwara and Schapira. (2) The Cohomologically Complete Nakayama Theorem. (3) A characterization of cohomologically cofinite complexes. (4) A theorem on completion by derived double centralizer. This is joint work with Marco Porta and Liran Shaul. Salle 001 Adresse IHP