Non-vanishing of the structure-sheaf cohomology of affine henselian schemes and henselian affinoids
Year: 2026
Type: preprint
Abstract: Let $(A,I)$ be a henselian pair such that $A$ is a domain of characteristic zero and $I\ne0$. We prove that any flat affine henselian scheme of finite presentation over $(A,I)$ has nonzero first structure-sheaf cohomology whenever one of its fibers over a point in $V(I)$ has positive dimension. This in particular gives a negative answer to the question by Devadas in the mixed-characteristic case. As an application, we also prove that the first structure-sheaf cohomology does not vanish for henselian affinoids of positive dimensions.
Source: arXiv (Cornell University)
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: 代数多様体上の複素・代数・算術力学系の深化と融合
OpenAlex ID: W7214680919