{
  "abstract": "There is a long tradition of constructing smooth projective varieties in positive characteristic with non-degenerate Hodge-to-de Rham spectral sequences. In this paper, we show that for any $n\\geq 1$ and any spot $(i, j)$ on the $E_n$-page, except for the cases where the differential is forced to be zero for trivial reasons, there exists a smooth projective variety whose Hodge-to-de Rham spectral sequence has a non-zero differential with source $E_n^{i, j}$. Our construction is inspired by constructions of nilmanifolds in complex geometry and can be regarded as a positive characteristic analogue.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35243",
  "author_total": 1,
  "authors": [
    {
      "name": "Kehao Cheng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3pxc8944z5dqz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35243",
  "fulltext_url": null,
  "id": "3pxc8944z5dqz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35243",
  "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"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7223799851",
  "pdf_url": "https://arxiv.org/pdf/2610.35243",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3pxc8944z5dqz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.35243",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35243"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The Hodge-to-de Rham spectral sequence can be arbitrarily non-degenerate in positive characteristic",
  "title_text": "The Hodge-to-de Rham spectral sequence can be arbitrarily non-degenerate in positive characteristic",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/3pxc8944z5dqz",
  "venue": "arXiv",
  "versions": []
}