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Title:Some Duality Results in Homological Algebra
Author(s):Richardson, Andrew S.
Doctoral Committee Chair(s):Griffith, Phillip A.
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Mathematics
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.
Issue Date:2002
Type:Text
Language:English
Description:156 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2002.
URI:http://hdl.handle.net/2142/86792
Other Identifier(s):(MiAaPQ)AAI3044207
Date Available in IDEALS:2015-09-28
Date Deposited:2002


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