Finiteness properties of extension functors of cofinite modules (Q2857007)

Let \(R\) be a Noetherian ring and \(I\) an ideal. An \(R\)-module \(M\) is said to be \(I\)-cofinite if \(\text{Supp} M \subset V(I)\) and \(\text{Ext}^i(R/I, M)\) are finitely generated for all \(i\). In the present paper, the authors consider the following question: Let \(M\) be an \(I\)-cofinite \(R\)-module. Are the \(R\)-module \(\text{Ext}^i(M, R/I)\) finitely generated for all \(i\)? They provide an affirmative answer if \(\dim M \leq 1\).