Cofiniteness and coassociated primes of local cohomology modules

TL;DR

This paper investigates the cofiniteness and coassociated primes of local cohomology modules over noetherian rings, providing characterizations and properties for modules with specific dimensional and finiteness conditions.

Contribution

It offers new characterizations of cofiniteness and coassociated primes of local cohomology modules, extending understanding to arbitrary ideals and modules beyond finiteness.

Findings

Characterization of $a$-cofinite artinian local cohomology modules.

Identification of coassociated primes of top local cohomology modules.

Results applicable to modules over rings with $ ext{dim } R/a=1$.

Abstract

Let $R$ be a noetherian ring, $\fa$ an ideal of $R$ such that $\dim R/\fa=1$ and $M$ a finite $R$--module. We will study cofiniteness and some other properties of the local cohomology modules $\lc^{i}_{\fa}(M)$. For an arbitrary ideal $\fa$ and an $R$--module $M$ (not necessarily finite), we will characterize $\fa$--cofinite artinian local cohomology modules. Certain sets of coassociated primes of top local cohomology modules over local rings are characterized.