ANNIHILATOR OF LOCAL COHOMOLOGY MODULES AND STRUCTURE OF RINGS

Tóm tắt

Let (R, m) be a Noetherian local ring, A an Artinian R-module, and M a finitely generated R-module. It is clear that Ann R(M/ p M) = p, for all p ∈ Var(Ann R M). Therefore, it is natural to consider the following dual property for annihilator of Artinian modules:

Ann R(0 : A p) = p, for all p ∈ Var(Ann R A). (∗)

Let i ≥ 0 be an integer. Alexander Grothendieck showed that the local cohomology module Hmi (M) of M is Artinian. The property (∗) of local cohomology modules is closed related to the structure of the base ring. In this paper, we prove that for each p ∈ Spec(R) such that Hmi (R/ p) satisfies the property (*) for all i, then R/ p is universally catenary and the formal fibre of R over p is Cohen-Macaulay.