Betti Numbers and Formal Local Cohomology Modules
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909726998003712 |
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| author | Sadeqi, Behruz |
| author_facet | Sadeqi, Behruz |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_05051 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Betti Numbers and Formal Local Cohomology Modules Sadeqi, Behruz Commutative Algebra 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. |
| title | Betti Numbers and Formal Local Cohomology Modules |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2508.05051 |