Cofiniteness of local cohomology modules for ideals of small dimension (Q1021438)

Let \((R,m)\) be a commutative Noetherian local ring and \(I\) a 1-dimensional ideal of \(R\). An \(R\)-module \(M\) is called \(I\)-cofinite, if \(\text{Supp}(M)\subseteq V(I)\) and \(\text{Ext}^{i}_{R}(R/I,M)\) is finitely generated for all \(i\). By Theorem 1.1 of [\textit{D. Delfino} and \textit{T. Marley}, J. Pure Appl. Algebra 121, No. 1, 45--52 (1997; Zbl 0893.13005)], we know that \(H^{i}_{I}(R):={\varinjlim}\text{Ext}^{i}_{R}(R/I^{n},R)\) are \(I\)-cofinite. The authors drop the local assumption of the mentioned result.