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