University of Illinois at Urbana-Champaign
Some Duality Results in Homological Algebra
Abstract
dc:descriptionFinally, we examine local cohomology involving square-free monomial ideals. We provide an alternate proof of one of Mustataˇ's constructions for computing H˙IR and use it to provide a simpler proof of E. Miller's duality result relating H˙IR to H˙m R/I , also showing that the latter result can be expressed in terms of the associated primes of H˙IR and the attached primes of H˙m R/I . To make this work, we prove a fairly general result regarding when the attached primes of a graded module are graded. We also investigate purely set-theoretic techniques for computing the local cohomology modules without recourse to linear algebra or symplectic geometry; these techniques can (when applicable) greatly improve computation time.
Degree
thesis:*- Name thesis:degree_name
- Ph.D.
- Level thesis:degree_level
- Dissertation
- Discipline thesis:degree_discipline
- Mathematics
- Grantor
- University of Illinois at Urbana-Champaign
- Year dc:date
- 2015
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Richardson, Andrew S.
- Contributors dc:contributor
-
- Griffith, Phillip A.
Subjects
dc:subject × 1Rights
- Language dc:language
- eng
Identifiers
dc:identifier.*- Identifier
- (MiAaPQ)AAI3044207
- OAI identifier oai:identifier
- oai:www.ideals.illinois.edu:2142/86792