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.

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:  13D45, 14B15, 13E05
DOI:  10.21136/CMJ.2017.0116-16

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Affiliations:   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

 
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