On the cofiniteness of small-level generalized local cohomology modules (Q779721)

Let \(R\) be a commutative Noetherian ring and let \(M\) and \(N\) be two finitely generated \(R\)-modules. In the paper under review, the authors prove the cofiniteness of generalized local cohomology modules \(H^i_{I}(M, N)\) with respect to \(I\) for all \(i< t\) and the finiteness of \((0 :_{H^t_I(M,N)} I)\) provided \(H^i_{I}(M, N)_{\mathfrak{p}}\) is finitely generated for all \(i < t\) and all \(\mathfrak{p}\in \cup_{j<t} \mathrm{Supp}_R(H^j_I (M, N))\) with \(\dim R/\mathfrak{p} > 1\), where \(t\) is a given non-negative integer.