A non-vanishing theorem for local cohomology modules (Q2447311)

Let \((R,\mathfrak{m})\) be a local Noetherian ring. In the paper under review the author introduces the class of weakly finite \(R\)-modules that is a generalization of the class of finitely generated \(R\)-modules and contains the classes of big Cohen-Macauly modules and \(\mathfrak{a}\)-cofinite modules for any ideal \(\mathfrak{a}\) of \(R\). Then the author improves the non-vanishing theorem due to Grothendieck for weakly finite modules.