Betti Numbers and Formal Local Cohomology Modules
Commutative Algebra
2025-08-08 v1
Abstract
This article investigates the relationship between Betti numbers of finitely generated modules over a Noetherian local ring and the structure of formal local cohomology modules. We establish a connection between the vanishing of formal local cohomology and the depth of a module, generalizing classical results. The main theorem links the Betti numbers to the Artinian property of formal local cohomology modules, and we provide applications to Cohen-Macaulay rings. Original proofs are given for all stated results.
Cite
@article{arxiv.2508.05051,
title = {Betti Numbers and Formal Local Cohomology Modules},
author = {Behruz Sadeqi},
journal= {arXiv preprint arXiv:2508.05051},
year = {2025}
}