20/04/2005, 11:00 — 12:00 — Room P3.10, Mathematics Building Gustavo Granja, Instituto Superior Técnico
Local cohomology as cellular approximation (Part I)
Given a perfect complex in the derived category of a ring one can define the categories of -torsion (respectively -complete modules). If and the ground ring is the integers these turn out to be the complexes which are quasi-isomorphic to complexes with -torsion homology (respectively -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 -modules (and local homology as Bousfield localization).
