Surjectivity of some local cohomology map and the second vanishing theorem

Surjectivity of some local cohomology map and the second vanishing theorem

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...

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Veröffentlicht in:Proceedings of the American Mathematical Society 2023-07, Vol.151 (7), p.2847-2862
Hauptverfasser: Asgharzadeh, Mohsen, Ishiro, Shinnosuke, Shimomoto, Kazuma
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creator Asgharzadeh, Mohsen
Ishiro, Shinnosuke
Shimomoto, Kazuma
description 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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