Off-campus UNL users: To download campus access dissertations, please use the following link to log into our proxy server with your NU ID and password. When you are done browsing please remember to return to this page and log out.

Non-UNL users: Please talk to your librarian about requesting this dissertation through interlibrary loan.

Asymptotic Growth of Stable Ext Modules

Matthew Bachmann, University of Nebraska - Lincoln

Abstract

Let R = Q/(f1,...,fc) where Q is a regular local ring and the fi form a regular sequence, and let M and N be finitely generated R-modules such that the lengths of the R-modules ExtR i (M,N) are finite for i sufficiently large. A result of Gulliksen implies that there exist polynomials such that governing the growth of the lengths of the even and odd Ext modules. Under these assumptions the stable cohomology modules will also have finite length for and be governed by polynomials in even and odd degrees. The focus of this thesis is to examine the relationship between the polynomials governing the lengths of the Ext-modules in large positive degrees and the polynomials governing the lengths of the stable cohomology modules in large negative degrees. We show that the polynomials have the same leading coefficient, depending on the parity of the codimension c. As an application of the result we show that the pairing hc(M,N) defined by Celikbas and Dao as a generalization of the Herbrand difference introduced by Buchweitz has the following properties:• if the embedding dimension of R is odd then hc(M,N) is alternating and hc(M,M) = 0.• if the embedding dimension of R is even then hc(M,N) is symmetric. (no equations included)

Subject Area

Mathematics|Theoretical Mathematics

Recommended Citation

Bachmann, Matthew, "Asymptotic Growth of Stable Ext Modules" (2023). ETD collection for University of Nebraska-Lincoln. AAI30574502.
https://digitalcommons.unl.edu/dissertations/AAI30574502

Share

COinS