Mathematics, Department of
First Advisor
L. L. Avramov
Second Advisor
S. B. Iyengar
Date of this Version
8-2017
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 $\mathbb{Z}$-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 $\mathfrak{m} M$, where $M$ is a finitely generated $R$-module and $\mathfrak{m}$ is the maximal homogeneous ideal of $R$, have infinite Castelnuovo-Mumford regularity.
Advisers: L. L. Avramov and S. B. Iyengar
Comments
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 L. L. Avramov and S. B. Iyengar Lincoln, Nebraska August, 2017
Copyright (c) 2017 Luigi Ferraro