Annihilators of local cohomology modules via a classification theorem of the dominant resolving subcategories

TL;DR

This paper explores conditions under which local cohomology modules have ideal-independent annihilators, utilizing Takahashi's classification of dominant resolving subcategories to establish new annihilation results in specific ring contexts.

Contribution

It applies Takahashi's classification theorem to identify when local cohomology modules have ideal-independent annihilators in finite-dimensional or Cohen-Macaulay rings.

Findings

Annihilators of local cohomology modules can be characterized using dominant resolving subcategories.

The classification theorem provides a framework for understanding annihilation in specific ring classes.

Results extend known properties of local cohomology to broader classes of rings.

Abstract

This paper investigates when local cohomology modules have an annihilator that does not depend on the choice of an ideal. Takahashi classified the dominant resolving subcategories of the category of finitely generated modules over a commutative Noetherian ring. We show that his classification theorem describes annihilation results of local cohomology modules over a finite-dimensional ring with certain assumptions or a Cohen-Macaulay ring.