Seminário de Álgebra 

20/04/2005, 11:00 — 12:00 — Sala P3.10, Pavilhão de Matemática
Gustavo Granja, Instituto Superior Técnico

Local cohomology as cellular approximation (Part I)

Given a perfect complex $A$ in the derived category of a ring one can define the categories of $A$-torsion (respectively $A$-complete modules). If $A=Z/p$ and the ground ring is the integers these turn out to be the complexes which are quasi-isomorphic to complexes with $p$-torsion homology (respectively $p$-complete homology). I will explain how one can use derived Morita theory to establish an equivalence between the triangulated categories of torsion and complete modules. I will then explain how Dwyer and Greenlees' use these ideas to interpret local cohomology as celullar approximation in the derived category of $R$-modules (and local homology as Bousfield localization).