Annihilators of local cohomology modules over a Cohen-Macaulay ring

Abstract

A lot of efforts have been put into determining which ideals annihilate local cohomology modules. Faltings' Annihilator Theorem ensured the existence of annihilators of local cohomology modules. In general, however, these annihilators depend on the choice of an ideal. This paper investigates the existence of annihilators of local cohomology modules without dependence on the choice of an ideal. Dao and Takahashi's classification theorem of dominant resolving subcategories helps observe the existence of annihilators over a finite-dimensional Cohen-Macaulay ring.