{
  "abstract": "Let $p$ be a prime. We construct a coherent formalism of geometric operations on Cartier modules with coefficients in ind-coherent sheaves on noetherian derived $\\mathbb F_p$-schemes. For such a scheme $X$, we consider the stable presentable category $\\mathrm{Cart}(X)$ of ind-coherent sheaves $M$ equipped with a structural morphism $F_{*,X}M \\to M$, where $F_X$ denotes the Frobenius endomorphism. We construct pushforward functors for arbitrary morphisms and exceptional pullback functors for separated morphisms almost of finite type, together with coherent composition and base-change equivalences. We single out conditions under which these functors admit further adjoints. On derived schemes separated and almost of finite type over $\\mathbb F_p$, we construct compatible closed symmetric monoidal structures given by shriek tensor products, and establish which functors are symmetric monoidal. The constructions arise from a general procedure for forming functor formalisms of Cartier objects, using their description as lax limits and the universal properties of span $2$-categories developed by Cnossen--Lenz--Linskens [arXiv:2505.19192].",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40200",
  "author_total": 2,
  "authors": [
    {
      "name": "Klaus Mattis"
    },
    {
      "name": "Timo Weiß"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7fn9wepc0tdtw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40200",
  "fulltext_url": null,
  "id": "7fn9wepc0tdtw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40200",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.CT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40200",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7fn9wepc0tdtw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.40200",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40200"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The $6\\frac{1}{2}$-functor formalism of Cartier modules",
  "title_text": "The 61/2-functor formalism of Cartier modules",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/7fn9wepc0tdtw",
  "venue": "arXiv",
  "versions": []
}