Annihilators of local cohomology modules via a classification theorem of the dominant resolving subcategories
Commutative Algebra
2021-08-27 v2
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.
Keywords
Cite
@article{arxiv.2105.00692,
title = {Annihilators of local cohomology modules via a classification theorem of the dominant resolving subcategories},
author = {Takeshi Yoshizawa},
journal= {arXiv preprint arXiv:2105.00692},
year = {2021}
}
Comments
10 pages; In the second version, minor revisions were made, including Remark 5.5