Abstract
Let $\frak a$ denote an ideal in a regular local (Noetherian) ring $R$ and let $N$ be a finitely generated $R$-module with support in $V(\frak a)$. The purpose of this paper is to show that all homomorphic images of the $R$-modules $\mathrm{Ext}^j_R(N, H^i_{\frak a}(R))$ have only finitely many associated primes, for all $i, j\geq 0$, whenever $\dim R \leq4$ or $\dim R/ \frak a \leq 3$ and $R$ contains a field. In addition, we show that if $\dim R=5$ and $R$ contains a field, then the $R$-modules $\mathrm{Ext}^j_R(N, H^i_{\frak a}(R))$ have only finitely many associated primes, for all $i, j\geq 0$.
Citation
Kamal BAHMANPOUR. Reza NAGHIPOUR. Monireh SEDGHI. "On the Finiteness Properties of Local Cohomology Modules for Regular Local Rings." Tokyo J. Math. 40 (1) 83 - 96, June 2017. https://doi.org/10.3836/tjm/1502179217