Publisher's Synopsis
Essentially two types of local cohomology have traditionally been considered in mathematics: geometric local cohomology, which is usually calculated through the derived functors of support functors, with respect to a locally closed subset of a locally noetherian scheme or topological space, and algebraic local cohomology, which may be described by the derived functors of torsion functors with respect to an ideal of a noetherian ring.;This book aims to give a self-contained presentation of the above topics, and shows how abstract localization techniques not only unify both points of view, while presenting new proofs of existing results, but also vastly enrich the theory. They do this by making it applicable to not necessarily a noetherian set-up, no longer restricted to locally closed supports or torsion with respect to ideals. Many applications are given to justify the new concepts and techniques introduced throughout the text.;The aim of this series is to disseminate important new material of a specialist nature in economic form. It ranges over the whole spectrum of mathematics and also reflects the changing momentum of dialogue between hitherto distinct areas of pure applied parts of the discipline.
