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.

Stable Cohomology of Local Rings and Castelnuovo-Mumford Regularity of Graded Modules

Luigi Ferraro, University of Nebraska - Lincoln

Abstract

This thesis consists of two parts: 1) A bimodule structure on the bounded cohomology of a local ring (Chapter 1), 2) Modules of infinite regularity over graded commutative rings (Chapter 2). ^ Chapter 1 deals with the structure of stable cohomology and bounded cohomology. Stable cohomology is a Z-graded algebra generalizing Tate cohomology and first defined by Pierre Vogel. It is connected to absolute cohomology and bounded cohomology. We investigate the structure of the bounded cohomology as a graded bimodule. We use the information on the bimodule structure of bounded cohomology to study the stable cohomology algebra as a trivial extension algebra and to study its commutativity. ^ In Chapter 2 it is proved that if a graded, commutative algebra R over a field k is not Koszul, then the nonzero modules mM, where M is a finitely generated R-module and m is the maximal homogeneous ideal of R, have infinite Castelnuovo-Mumford regularity. ^

Subject Area

Mathematics

Recommended Citation

Ferraro, Luigi, "Stable Cohomology of Local Rings and Castelnuovo-Mumford Regularity of Graded Modules" (2017). ETD collection for University of Nebraska - Lincoln. AAI10615063.
http://digitalcommons.unl.edu/dissertations/AAI10615063

Share

COinS