{
  "abstract": "Let $k=\\overline{\\mathbb{F}_2}$. We construct a nine-dimensional $F$-rational affine variety $X$ admitting a locally closed embedding $X\\hookrightarrow \\mathbb{P}_k^{19}$ together with a dense open set $U\\subseteq (\\mathbb{P}^{19})^\\vee$ such that $X\\cap H$ is not $F$-rational (or even $F$-injective) for all $H\\in U$. We also construct a nine-dimensional projective $F$-rational variety $\\mathfrak{X}$ and a closed embedding $\\mathfrak{X}\\hookrightarrow\\mathbb{P}^{29}_k$ under which the same conclusion holds.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18921",
  "author_total": 2,
  "authors": [
    {
      "name": "Thomas Polstra"
    },
    {
      "name": "Austyn Simpson"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4e2p5gz70spcz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18921",
  "fulltext_url": null,
  "id": "4e2p5gz70spcz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18921",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AC"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7213528957",
  "pdf_url": "https://arxiv.org/pdf/2609.18921",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4e2p5gz70spcz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.18921",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18921"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Bertini's theorem for $F$-rationality is false",
  "title_text": "Bertini's theorem for F-rationality is false",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/4e2p5gz70spcz",
  "venue": "arXiv",
  "versions": []
}