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June 2017 On the Finiteness Properties of Local Cohomology Modules for Regular Local Rings
Kamal BAHMANPOUR, Reza NAGHIPOUR, Monireh SEDGHI
Tokyo J. Math. 40(1): 83-96 (June 2017). DOI: 10.3836/tjm/1502179217

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

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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

Information

Published: June 2017
First available in Project Euclid: 8 August 2017

zbMATH: 06787089
MathSciNet: MR3689980
Digital Object Identifier: 10.3836/tjm/1502179217

Subjects:
Primary: 13D45
Secondary: 13H05, 14B15

Rights: Copyright © 2017 Publication Committee for the Tokyo Journal of Mathematics

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Vol.40 • No. 1 • June 2017
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