Geodesic
Cofiniteness and finiteness of local cohomology modules over regular local rings
Czechoslovak Mathematical Journal, Tome 67 (2017) no. 3, pp. 733-740.

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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.
DOI : 10.21136/CMJ.2017.0116-16
Classification : 13D45, 13E05, 14B15
Keywords: cofinite module; Cohen-Macaulay ring; Krull dimension; local cohomology; regular ring 
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     title = {Cofiniteness and finiteness of local cohomology modules over regular local rings},
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A'zami, Jafar; Pourreza, Naser. Cofiniteness and finiteness of local cohomology modules over regular local rings. Czechoslovak Mathematical Journal, Tome 67 (2017) no. 3, pp. 733-740. doi : 10.21136/CMJ.2017.0116-16. http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2017.0116-16/

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