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.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:568607 |
| Date | January 2013 |
| Creators | Mckemey, Robert |
| Contributors | Symonds, Peter |
| Publisher | University of Manchester |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | https://www.research.manchester.ac.uk/portal/en/theses/relative-local-cohomology(9eb51c32-c86b-46db-8c80-391ce9390370).html |
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