Effective generic freeness and applications to local cohomology
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866914910487707648 |
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| author | Cid-Ruiz, Yairon Smirnov, Ilya |
| author_facet | Cid-Ruiz, Yairon Smirnov, Ilya |
| contents | Let $A$ be a Noetherian domain and $R$ be a finitely generated $A$-algebra. We study several features regarding the generic freeness over $A$ of an $R$-module. For an ideal $I \subset R$, we show that the local cohomology modules ${\rm H}_I^i(R)$ are generically free over $A$ under certain settings where $R$ is a smooth $A$-algebra. By utilizing the theory of Gröbner bases over arbitrary Noetherian rings, we provide an effective method to make explicit the generic freeness over $A$ of a finitely generated $R$-module. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_08196 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Effective generic freeness and applications to local cohomology Cid-Ruiz, Yairon Smirnov, Ilya Commutative Algebra Algebraic Geometry Let $A$ be a Noetherian domain and $R$ be a finitely generated $A$-algebra. We study several features regarding the generic freeness over $A$ of an $R$-module. For an ideal $I \subset R$, we show that the local cohomology modules ${\rm H}_I^i(R)$ are generically free over $A$ under certain settings where $R$ is a smooth $A$-algebra. By utilizing the theory of Gröbner bases over arbitrary Noetherian rings, we provide an effective method to make explicit the generic freeness over $A$ of a finitely generated $R$-module. |
| title | Effective generic freeness and applications to local cohomology |
| topic | Commutative Algebra Algebraic Geometry |
| url | https://arxiv.org/abs/2302.08196 |