{
  "abstract": "We introduce the notion of Hodge--Tate splitting for schemes in positive characteristic. For a smooth variety $X$ over a perfect field $k$ of characteristic $p > 0$, we say that $X$ is Hodge--Tate split if the natural morphism $\\mathcal{O}_X \\to F_*Ω^\\bullet_{X/k}$ induced by the absolute Frobenius admits a splitting in $\\mathcal{D}_{\\mathrm{qcoh}}(X)$. We prove that this condition is equivalent to the existence of a decomposition $F_*Ω^\\bullet_{X/k} \\simeq \\bigoplus_{i=0}^{\\dim X}Ω^i_{X/k}[-i]$ of its de Rham complex. Consequently, for smooth projective varieties, Hodge--Tate splitting implies Akizuki--Nakano vanishing and the $E_1$-degeneration of the Hodge-to-de Rham spectral sequence. Furthermore, we establish criteria and permanence properties for Hodge--Tate splitting and use them to construct many new examples of varieties whose de Rham complexes decompose. These include blow-ups of quasi-$F$-split varieties along strata of simple normal crossings divisors, complete intersections in toric varieties, and linearly reductive quotients of Hodge--Tate split varieties. Among these examples, we obtain smooth projective varieties whose Hodge-to-de Rham spectral sequences degenerate at $E_1$, whereas their Hochschild--Kostant--Rosenberg spectral sequences do not degenerate. As an application in mixed characteristic, we prove an Akizuki--Nakano-type vanishing theorem for smooth projective globally $+$-regular varieties over the Witt ring of a perfect field.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.00567",
  "author_total": 2,
  "authors": [
    {
      "name": "Ryo Ishizuka"
    },
    {
      "name": "Shou Yoshikawa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dfe5c2cc14rcy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.00567",
  "fulltext_url": null,
  "id": "dfe5c2cc14rcy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.00567",
  "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.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7206178192",
  "pdf_url": "https://arxiv.org/pdf/2609.00567",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dfe5c2cc14rcy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2609.00567",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.00567"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Hodge--Tate splitting and Akizuki--Nakano vanishing in positive characteristic",
  "title_text": "Hodge--Tate splitting and Akizuki--Nakano vanishing in positive characteristic",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/dfe5c2cc14rcy",
  "venue": "arXiv",
  "versions": []
}