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Cofiniteness of local cohomology modules for ideals of small dimension. (English) Zbl 1168.13016
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 [D. Delfino and 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.

MSC:
13D45 Local cohomology and commutative rings
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