Cofiniteness and coassociated primes of local cohomology modules

Abstract

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