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arXiv · 2107.09041

Surjectivity of some local cohomology map and the second vanishing theorem

Mohsen Asgharzadeh·Shinnosuke Ishiro·Kazuma Shimomoto
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Abstract

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.

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Mohsen Asgharzadeh, Shinnosuke Ishiro, Kazuma Shimomoto. 2022-10-12. Surjectivity of some local cohomology map and the second vanishing theorem. https://doi.org/10.1090/proc%2F16340

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