مشخصات پژوهش

Let R denote a commutative Noetherian ring, a an ideal of R, and M an a-cofinite R-module. The purpose of this article is to show that for a positive integer t, the R-module Hia (M) is finitely generated for all i < t if and only if the Rp-module Hi aRp(Mp) is finitely generated for all i < t and all p ∈ Spec(R). As a consequence, we provide a generalization and short proof of Faltings’ local–global principle for finiteness dimensions; i.e., fa(M) = inf{faRp(Mp)| p ∈ Spec(R)}.