## Tokyo Journal of Mathematics

### On the Finiteness Properties of Local Cohomology Modules for Regular Local Rings

#### 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 $i, j\geq 0$.

#### Article information

Source
Tokyo J. Math., Volume 40, Number 1 (2017), 83-96.

Dates
First available in Project Euclid: 8 August 2017

https://projecteuclid.org/euclid.tjm/1502179217

Digital Object Identifier
doi:10.3836/tjm/1502179217

Mathematical Reviews number (MathSciNet)
MR3689980

Zentralblatt MATH identifier
06787089

#### Citation

SEDGHI, Monireh; BAHMANPOUR, Kamal; NAGHIPOUR, Reza. On the Finiteness Properties of Local Cohomology Modules for Regular Local Rings. Tokyo J. Math. 40 (2017), no. 1, 83--96. doi:10.3836/tjm/1502179217. https://projecteuclid.org/euclid.tjm/1502179217

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