{
  "abstract": "Shimada recently showed that Frobenius--Witt cotangent complex, the animation of Saito's Frobenius--Witt differentials, vanishes on perfectoid rings, thus it serves as a candidate of ``absolute'' cotangent complex. In this article, we give a pullback description of their arithmetic extension, and as a consequence, we give a direct description of Frobenius--Witt cotangent complex, which leads to generalizations to derived rings and animated pre-log rings. This description allows us to compute Frobenius--Witt cotangent complex of derived $δ$-rings as well. We also propose a version of Frobenius--Witt cotangent complex relative to derived $δ$-rings, and establish a vanishing result for prisms, which generalizes vanishing of Frobenius--Witt cotangent complex of perfectoid rings. Finally, independently of previous considerations, we give a regularity criterion via Frobenius--Witt cotangent complex for $p$-local Noetherian (not necessarily local) rings without $F$-finiteness. We also record the flatness of Frobenius--Witt cotangent complex of valuation rings, with essential ideas due to ChatGPT-6 Astra.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.04487",
  "author_total": 1,
  "authors": [
    {
      "name": "Zhouhang Mao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1jc3f9fhbjvw8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.04487",
  "fulltext_url": null,
  "id": "1jc3f9fhbjvw8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.04487",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AC"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.AT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7197041690",
  "pdf_url": "https://arxiv.org/pdf/2608.04487",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1jc3f9fhbjvw8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:57Z",
      "native_id": "2608.04487",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.04487"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Frobenius--Witt cotangent complex for derived rings",
  "title_text": "Frobenius--Witt cotangent complex for derived rings",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:57Z",
  "url": "https://research.draconitic.com/paper/1jc3f9fhbjvw8",
  "venue": "arXiv",
  "versions": []
}