Relative Local Cohomology

Abstract

This thesis will examine Relative Local Cohomology. First we extend many well known theorems about Local Cohomology of finitely generated modules with respect to an ideal of a commutative noetherian rings so that they hold for non-finitely generated modules with respect to certain ideals of non-commutative non-noetherian rings. Then we show how similar results hold for Relative Local Cohomology. In particular we provide a relative version of the Local Duality Theorem. We then examine the links between Relative Homological Algebra and the concept of Structure Theorems and give a bound on the Castelnuovo-Mumford Regularity of rings of invariants based on the Cech Complex.

Date of Award	28 Nov 2012
Original language	English
Awarding Institution	The University of Manchester