A new proof of Faltings' local-global principle for the finiteness of local cohomology modules

摘要

Let R be a commutative Noetherian ring, and let be ideals of R. The goal of this paper is to show that, for a finitely generated R-module M, if the set is finite or , then , where denotes the first non -cofiniteness of the local cohomology module . As a consequence of this, we provide a new and short proof of the Faltings' local-global principle for finiteness dimensions. Also, several new results concerning the finiteness dimensions are given.