{
  "abstract": "This article is the second of three articles whose goal is to generalize the Cartier transform of Ogus and Vologodsky to the logarithmic setting. We generalize a topos-theoretic version of this transform, due to Oyama. Let $k$ be a perfect field of positive characteristic $p$ and equip $S=\\operatorname{Spec}k$ with the trivial log structure. For a log smooth morphism of logarithmic schemes $X \\rightarrow S,$ we construct crystalline-like ringed topoi $\\mathcal{E}'$ and $\\underline{\\mathcal{E}}$ and subcategories of crystals of quasi-coherent modules $\\mathcal{C}'$ and $\\underline{\\mathcal{C}},$ equivalent respectively, under some lifting assumption, to modules with Higgs fields and integrable connections, both satisfying certain nilpotence conditions, and a morphism of topoi $\\underline{\\mathcal{E}} \\rightarrow \\mathcal{E}'.$ We then prove that the pullback functor of this morphism of topoi preserves quasi-coherent crystals and hence induces a functor $\\mathcal{C}' \\rightarrow \\underline{\\mathcal{C}},$ generalizing the Cartier transform. We finally use a log flat descent theorem for morphisms, that we proved in the first article, to prove that this functor is fully faithful.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27549",
  "author_total": 1,
  "authors": [
    {
      "name": "Sami Fersi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e6w875752sgm7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27549",
  "fulltext_url": null,
  "id": "e6w875752sgm7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27549",
  "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": "W7214187802",
  "pdf_url": "https://arxiv.org/pdf/2609.27549",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e6w875752sgm7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27549",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27549"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A Topos-Theoretic Approach to the Logarithmic Cartier Transform",
  "title_text": "A Topos-Theoretic Approach to the Logarithmic Cartier Transform",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/e6w875752sgm7",
  "venue": "arXiv",
  "versions": []
}