The derived category analogue of some results in local cohomology
In the paper under review, the authors provide the derived category analogue of some results about the local cohomology modules. The main result says that: Theorem. Let \(R\) be a commutative Noetherian ring with finite number of maximal ideals. Let \(Z\) be a subset of Spec\((R)\) that is stable under specialization. Then for any left bounded complex \(X\) of \(R\)-modules with finitely generated homology, the following equality holds: \(\mathrm{inf }\{i| H^i_Z (X)\) is not Artinian\(\}=\mathrm{inf }\{\mathrm{depth}_{R_p} X_p| p\in \mathrm{Z-Max }R\}\).
scientific article; zbMATH DE number 6838833
scientific article