{
  "abstract": "Let $k$ be a perfect field of characteristic $p>0$. Ekedahl proved an equivalence of triangulated categories between bounded coherent complexes over the Raynaud ring and complexes of $F$-gauges. We give a geometric proof, independent of his proof, that the de Rham-Witt realization is a symmetric monoidal equivalence of stable $\\infty$-categories between perfect $F$-gauges and bounded coherent complexes over the Raynaud ring with Ekedahl's completed star product, as expected by Illusie. The geometry comes from topological restriction homology: $\\mathrm{TR}^r(k;\\mathbf Z_p)^{hS^1}$ is an iterated fibre product of copies of $\\mathrm{TC}^-(k;\\mathbf Z_p)$, and taking even stacks before and after the fibre product gives the genuine and the naive $r$-Nygaard stacks. Pushforward from the genuine to the naive $r$-Nygaard stack realizes Andriopoulos' $r$-Nygaard filtrations, which interpolate between the Nygaard filtration at $r=1$ and the Hodge-Witt filtration at $r=\\infty$. On the genuine $r$-Nygaard stack, which is a chain of Nygaard charts, restriction and Frobenius come from the inclusions of sub-chains, Verschiebung from duality, and the differential as a Bockstein operator, and the relations of the star product become projection formulas. As applications, we deduce Ekedahl's Künneth formula and Poincaré duality for de Rham-Witt cohomology from their counterparts for $F$-gauge cohomology, and show that the special-value formulas of Illusie and of Mondal over finite fields are equivalent.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28149",
  "author_total": 1,
  "authors": [
    {
      "name": "Yuanning Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1wgasmwxavehj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28149",
  "fulltext_url": null,
  "id": "1wgasmwxavehj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28149",
  "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"
    ],
    [
      "arxiv",
      "math.AT"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7223109188",
  "pdf_url": "https://arxiv.org/pdf/2610.28149",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1wgasmwxavehj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.28149",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28149"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The stacky approach to de Rham-Witt cohomology",
  "title_text": "The stacky approach to de Rham-Witt cohomology",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/1wgasmwxavehj",
  "venue": "arXiv",
  "versions": []
}