Modules of Finite Projective Dimension and Singularities

Authors

Nawaj KC, University of Nebraska-LincolnFollow

First Advisor

Jack Jeffries

Second Advisor

Mark Walker

Degree Name

Doctor of Philosophy (Ph.D.)

Department

Mathematics

Date of this Version

5-2025

Document Type

Dissertation

Citation

A dissertation presented to the faculty of the Graduate College at the University of Nebraska in partial fulfillment of requirements for the degree of Doctor of Philosophy

Major: Mathematics

Under the supervision of Professors Jack Jeffries and Mark Walker

Lincoln, Nebraska, May 2025

Comments

Copyright 2025, Nawaj KC. Used by permission

Abstract

In the first part of this thesis, we study liftings of modules of finite projective dimension. We introduce a notion of “Serre liftable” modules and deduce applications to multiplicity conjectures in local algebra. In the second part, we introduce and study a module of mixed K\"ahler differentials for finite algebras over ramified discrete valuation rings of mixed characteristic. We state and prove a Jacobian criterion for computing the singular loci of such algebras.

Advisors: Jack Jeffries and Mark Walker

Recommended Citation

KC, Nawaj, "Modules of Finite Projective Dimension and Singularities" (2025). Dissertations and Doctoral Documents from University of Nebraska-Lincoln, 2023–. 308.
https://digitalcommons.unl.edu/dissunl/308