Surjectivity of some local cohomology map and the second vanishing theorem
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2021
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| _version_ | 1866915824785162240 |
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| author | Asgharzadeh, Mohsen Ishiro, Shinnosuke Shimomoto, Kazuma |
| author_facet | Asgharzadeh, Mohsen Ishiro, Shinnosuke Shimomoto, Kazuma |
| contents | The second vanishing theorem has a long history in the theory of local cohomology modules, which connects the vanishing of a complete regular local ring with a topological property of the punctured spectrum of the ring under some conditions. However, the case of complete ramified regular local rings is unresolved. In this paper, we give a partial answer to the second vanishing theorem in the ramified case. Our proof is inspired by the theory of surjective elements in the theory of local cohomology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_09041 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Surjectivity of some local cohomology map and the second vanishing theorem Asgharzadeh, Mohsen Ishiro, Shinnosuke Shimomoto, Kazuma Commutative Algebra Algebraic Geometry The second vanishing theorem has a long history in the theory of local cohomology modules, which connects the vanishing of a complete regular local ring with a topological property of the punctured spectrum of the ring under some conditions. However, the case of complete ramified regular local rings is unresolved. In this paper, we give a partial answer to the second vanishing theorem in the ramified case. Our proof is inspired by the theory of surjective elements in the theory of local cohomology. |
| title | Surjectivity of some local cohomology map and the second vanishing theorem |
| topic | Commutative Algebra Algebraic Geometry |
| url | https://arxiv.org/abs/2107.09041 |