{
  "abstract": "For any regular projective surface $X$ over an arbitrary field $k$ of characteristic $p>0$ with $K_X\\equiv0$, we prove that \\[ 60K_X\\sim0 . \\] This uniform bound is optimal. To show that the factor $5$ is necessary, we construct an example in characteristic $5$ for which $K_X$ has exact order five. If $X$ is geometrically normal, then $12K_X\\sim0$. Our main focus is the geometrically non-normal case, where we obtain more precise bounds according to the Albanese morphism. If it is nontrivial, then $p=2$ or $3$, and we prove $12K_X\\sim0$ and $6K_X\\sim0$, respectively; both bounds are optimal. If it is trivial, then $K_X\\sim0$ for $p\\ge7$, while $5K_X\\sim0$, $3K_X\\sim0$, and $4K_X\\sim0$ for $p=5,3,2$, respectively.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.09542",
  "author_total": 3,
  "authors": [
    {
      "name": "Jingshan Chen"
    },
    {
      "name": "Chongning Wang"
    },
    {
      "name": "Lei Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ar0y8hj8xmvgx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09542",
  "fulltext_url": null,
  "id": "ar0y8hj8xmvgx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.09542",
  "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.AG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7221054176",
  "pdf_url": "https://arxiv.org/pdf/2610.09542",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ar0y8hj8xmvgx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.09542",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09542"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Effective nonvanishing of $K$-trivial regular surfaces over imperfect fields",
  "title_text": "Effective nonvanishing of K-trivial regular surfaces over imperfect fields",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/ar0y8hj8xmvgx",
  "venue": "arXiv",
  "versions": []
}