Cofiniteness and vanishing of local cohomology modules, and colength of conductor ideals

Donatella Delfino, Purdue University

Abstract

In Chapter 1 we prove a special case of a conjecture by Huneke and Lyubeznik about the vanishing of local cohomology modules. In Chapter 2 we prove that, if M is a module over a complete noetherian local ring R and if I is an ideal, then $H\sbsp{I}{j}(M)$ is I-cofinite if R is either equicharacteristic, or Cohen-Macaulay, or if the uniformizing parameter of a coefficeint ring of R is in $\sqrt{I}$. In Chapter 3 we give equivalent conditions for a one-dimensional local, reduced, excellent ring R to be such that $t\lambda(R/{\cal C}) - \lambda(\overline{R}$/R) = a (where a $\in\rm I\!N$ is fixed), t = e $-$ 1 and t $\ge$ a. Here t is the Cohen-Macaulay type of R, e is the multiplicity, $\lambda(-)$ is the length of R-modules, $\overline{R}$ is the integral closure of R in its total quotient ring, and ${\cal C}$ is the conductor of R in $\overline{R}.$

Degree

Ph.D.

Advisors

Huneke, Purdue University.

Subject Area

Mathematics

COinS