{
  "abstract": "We investigate the permanence of local stability for one-parameter families $X\\to C$ under finite flat base-changes, when the base-field has positive characteristic $p>0$. Building on previous work of Hu--Zong, we show that it suffices to consider base-changes by Frobenius morphisms. In that case, we show that the situation is governed by the discrepancies of the pairs $(X,X_c)$, together with some differential invariants of the vertical divisors whose multiplicity in their fiber is divisible by $p$. While the behaviour of these invariants remains in general mysterious, we establish upper bounds under some $F$-splitting assumptions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.22106",
  "author_total": 2,
  "authors": [
    {
      "name": "Marta Benozzo"
    },
    {
      "name": "Quentin Posva"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/94kgawp56dtcb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.22106",
  "fulltext_url": null,
  "id": "94kgawp56dtcb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.22106",
  "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.AG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7171389432",
  "pdf_url": "https://arxiv.org/pdf/2607.22106",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/94kgawp56dtcb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2607.22106",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.22106"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Base-change of locally stable families in positive characteristic",
  "title_text": "Base-change of locally stable families in positive characteristic",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/94kgawp56dtcb",
  "venue": "arXiv",
  "versions": []
}