Matlis duals of top Local Cohomology Modules

TL;DR

This paper investigates the properties of Matlis duals of local cohomology modules, providing new generalizations and explicit computations of associated primes in specific algebraic settings.

Contribution

It introduces a novel technique for analyzing associated primes of Matlis duals and computes these primes for certain local cohomology modules in local rings.

Findings

Generalizations of associated primes of Matlis duals proved

Explicit description of associated primes for specific local cohomology modules

New technique enhances understanding of duality in local cohomology

Abstract

In the first section of this paper we present generalizations of known results on the set of associated primes of Matlis duals of local cohomology modules; we prove these generalizations by using a new technique. In section 2 we compute the set of associated primes of the Matlis dual of $\LCMo ^{d-1}_J(R)$, where $R$ is a $d$-dimensional local ring and $J\subseteq R$ an ideal such that $\dim (R/J)=1$ and $\LCMo ^d_J(R)=0$.