2021/07/19 by Asgharzadeh, Mohsen, Ishiro, Shinnosuke, Shimomoto, Kazuma
#Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.2107.09041
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.