Czechoslovak Mathematical Journal, Vol. 67, No. 3, pp. 733-740, 2017

Cofiniteness and finiteness of local cohomology modules over regular local rings

Jafar A'zami, Naser Pourreza

Received March 8, 2016.   First published March 27, 2017.

Jafar A'zami (corresponding author), Naser Pourreza, Department of Mathematics, Faculty of Mathematical Sciences, University of Mohaghegh Ardabili, Daneshgah Street, Ardabil, 56199-11367, Iran, e-mail: jafar.azami@gmail.com, azami@uma.ac.ir, pourreza1974@gmail.com

Abstract: Let $(R,\mathfrak m)$ be a commutative Noetherian regular local ring of dimension $d$ and $I$ be a proper ideal of $R$ such that ${\rm mAss}_R(R/I)={\rm Assh}_R(I)$. It is shown that the $R$-module $H^{{\rm ht}(I)}_I(R)$ is $I$-cofinite if and only if ${\rm cd}(I,R)={\rm ht}(I)$. Also we present a sufficient condition under which this condition the $R$-module $H^i_I(R)$ is finitely generated if and only if it vanishes.

Keywords: cofinite module; Cohen-Macaulay ring; Krull dimension; local cohomology; regular ring

Classification (MSC 2010): 13D45, 14B15, 13E05

DOI: 10.21136/CMJ.2017.0116-16

Full text available as PDF.


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