Modules with Finite Cousin Cohomologies Have Uniform Local Cohomological Annihilators

TL;DR

This paper proves that finite modules over Noetherian rings with finite Cousin complex cohomologies possess uniform local cohomological annihilators, linking cohomological properties with module structure.

Contribution

It establishes a new equivalence between finite Cousin complex cohomologies and the existence of uniform local cohomological annihilators under certain conditions.

Findings

Finite modules with finite Cousin cohomologies have uniform local cohomological annihilators.

The converse holds for modules satisfying (S_2) over local rings with Cohen-Macaulay formal fibres.

Provides a characterization connecting Cousin cohomologies and local cohomological annihilators.

Abstract

Let A be a Noetherian ring. It is shown that any finite A--module M of finite Krull dimension with finite Cousin complex cohomologies has a uniform local cohomological annihilator. The converse is also true for a finite module M satisfying (S_2) which is over a local ring with Cohen--Macaulay formal fibres.