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arXiv · 2508.05051

Betti Numbers and Formal Local Cohomology Modules

Behruz Sadeqi
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Abstract

This article investigates the relationship between Betti numbers of finitely generated modules over a Noetherian local ring $(R, \mathfrak{m})$ 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.

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Behruz Sadeqi. 2025-08-07. Betti Numbers and Formal Local Cohomology Modules. https://arxiv.org/abs/2508.05051

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