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https://hdl.handle.net/2142/86792
Description
Title
Some Duality Results in Homological Algebra
Author(s)
Richardson, Andrew S.
Issue Date
2002
Doctoral Committee Chair(s)
Griffith, Phillip A.
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
Abstract
Finally, 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.
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