Repository logo
 

Finitely generated modules over Noetherian rings: interactions between algebra, geometry, and topology

Simple item page
dc.contributor.authorFlores, Zachary J., author
dc.contributor.authorPeterson, Christopher, advisor
dc.contributor.authorDuflot, Jeanne, committee member
dc.contributor.authorCavalieri, Renzo, committee member
dc.contributor.authorRoss, Kathryn, committee member
dc.date.accessioned2020-08-31T10:11:52Z
dc.date.available2020-08-31T10:11:52Z
dc.date.issued2020
dc.description.abstractIn this dissertation, we aim to study finitely generated modules over several different Noetherian rings and from varying perspectives. This work is divided into four main parts: The first part is a study of algebraic K-theory for a certain class of local Noetherian rings; the second discusses extending well-known results on Lefschetz properties for graded complete intersection algebras to a class of graded finite length modules using geometric techniques; the third discusses the structure of various algebraic and geometric invariants attached to the finite length modules from the previous section; and lastly, we discuss the structure of annihilating ideals of classes of hyperplane arrangements in projective space.
dc.format.mediumborn digital
dc.format.mediumdoctoral dissertations
dc.identifierFLORES_colostate_0053A_16113.pdf
dc.identifier.urihttps://hdl.handle.net/10217/211775
dc.languageEnglish
dc.language.isoeng
dc.publisherColorado State University. Libraries
dc.relation.ispartof2020-
dc.rightsCopyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.
dc.subjectalgebraic K-theory
dc.subjectcommutative algebra
dc.subjectLefschetz properties
dc.subjectapolar algebras
dc.subjectalgebraic geometry
dc.subjecthyperplane arrangements
dc.titleFinitely generated modules over Noetherian rings: interactions between algebra, geometry, and topology
dc.typeText
dcterms.rights.dplaThis Item is protected by copyright and/or related rights (https://rightsstatements.org/vocab/InC/1.0/). You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
thesis.degree.disciplineMathematics
thesis.degree.grantorColorado State University
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy (Ph.D.)

Files

Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
FLORES_colostate_0053A_16113.pdf
Size:
606.22 KB
Format:
Adobe Portable Document Format
Download

Collections

2020-
Theses and Dissertations