Top Local Cohomology Modules Are Almost Always Non-Artinian

Abstract

Let $(R,\mathfrak{m})$ be a Noetherian local ring, $I$ an ideal of $R$ and $M$ a weakly finite or a coatomic $R$-module of dimension $n$. In this article, we resolve the Artinianness and non-Artinianness of top local cohomology modules, $H_I^{cd(I,M)}(M)$, in all cases except in the case $cd(I,M)=n-1$ and $dim(R/I+Ann(M))>1$ for which we have some sorter results under certain conditions.

This paper has been withdrawn by the authors due to an error in the proof of the main theorem

References in corpus (1)

• On The Cohomological Dimension of Local Cohomology Modules