Surjectivity of some local cohomology map and the second vanishing theorem
Commutative Algebra
2026-03-03 v4 Algebraic Geometry
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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@article{arxiv.2107.09041,
title = {Surjectivity of some local cohomology map and the second vanishing theorem},
author = {Mohsen Asgharzadeh and Shinnosuke Ishiro and Kazuma Shimomoto},
journal= {arXiv preprint arXiv:2107.09041},
year = {2026}
}
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