Finitely generated modules over Noetherian rings: interactions between algebra, geometry, and topology
Date
2020
Authors
Flores, Zachary J., author
Peterson, Christopher, advisor
Duflot, Jeanne, committee member
Cavalieri, Renzo, committee member
Ross, Kathryn, committee member
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Abstract
In 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.
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Subject
algebraic K-theory
commutative algebra
Lefschetz properties
apolar algebras
algebraic geometry
hyperplane arrangements