{
  "abstract": "This article is the first of three articles whose goal is to generalize the Cartier transform of Ogus and Vologodsky to the logarithmic setting. In this article, we generalize a local version, due to Shiho, of the Cartier transform to log smooth schemes. More precisely, let $k$ be a perfect field of positive characteristic and equip $\\operatorname{Spec}k$ with the trivial logarithmic structure. For a log smooth morphism of logarithmic schemes $X \\rightarrow S,$ where $S$ is log flat and locally of finite type over $\\operatorname{Spec}k,$ we obtain, under the assumption that the exact relative Frobenius lifts over the Witt vectors of $k$ to a morphism between log smooth schemes over $S,$ a fully faithful functor from the category of quasi-coherent modules on the base change $X'=X\\times_{S,F_S}S$ of $X$ by the Frobenius $F_S$ of $S,$ equipped with a quasi-nilpotent Higgs field, to the category of quasi-coherent modules on $X$ equipped with a quasi-nilpotent integrable connection. For this, we prove a log flat descent theorem for morphisms, based on previous work by Kato.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25172",
  "author_total": 1,
  "authors": [
    {
      "name": "Sami Fersi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3te92ncpwct7e.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25172",
  "fulltext_url": null,
  "id": "3te92ncpwct7e",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25172",
  "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": "W7214071160",
  "pdf_url": "https://arxiv.org/pdf/2609.25172",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3te92ncpwct7e.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.25172",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25172"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Local Logarithmic Cartier Transform",
  "title_text": "Local Logarithmic Cartier Transform",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/3te92ncpwct7e",
  "venue": "arXiv",
  "versions": []
}