A new version of Local-Global Principle for annihilations of local cohomology modules

Abstract

Let R be a commutative Noetherian ring. Let a and b be ideals of R and let N be a finitely generated R-module. We introduce a generalization of the b-finiteness dimension of f b a (N ) relative to a in the context of generalized local cohomology modules aswhere M is an R-module. We also show that f b a (N ) ≤ f b a (M, N ) for any R-module M . This yields a new version of the Local-Global Principle for annihilation of local cohomology modules. Moreover, we obtain a generalization of the Faltings Lemma.

On conjectures of Hovey--Strickland and Chai

“…Proof. This result follows from the implication (c) =⇒ (a) of Theorem 2.9 in [KYA04]; we include an independent argument here. Consider the derived functor on the derived category of R-modules…”