{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30851",
  "author_total": 3,
  "authors": [
    {
      "name": "Yoshinori Gongyo"
    },
    {
      "name": "Fumiharu Kato"
    },
    {
      "name": "Takayuki Uchiba"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/esvy3epa35hbc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30851",
  "fulltext_url": null,
  "id": "esvy3epa35hbc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30851",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AC"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7214680919",
  "pdf_url": "https://arxiv.org/pdf/2609.30851",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/esvy3epa35hbc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.30851",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30851"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Non-vanishing of the structure-sheaf cohomology of affine henselian schemes and henselian affinoids",
  "title_text": "Non-vanishing of the structure-sheaf cohomology of affine henselian schemes and henselian affinoids",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/esvy3epa35hbc",
  "venue": "arXiv",
  "versions": []
}