{
  "abstract": "Let $A$ be a finite Hopf algebra over a Noetherian commutative ring $R$. For any map $f : R \\to k$ where $k$ is a field, there is a natural map on the cohomology of $A$ under this change of coefficients $H^\\ast(f): H^\\ast(A, R) \\otimes_R k \\to H^\\ast(A_k, k)$. In this paper we examine this map for $R = \\mathbb Z[ζ]$ the cyclotomic integers with $ζ$ an $\\ell$th root of unity. We show that under a finite generation assumption, the induced map gives a homeomorphism on the spectra of the two cohomology rings. Finally, we turn to small quantum groups defined over $\\mathbb Z[ζ]$ and show that, with mild restrictions on $\\ell$, every fiber map whose residue field has a good prime characteristic induces an isomorphism on cohomology.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37693",
  "author_total": 1,
  "authors": [
    {
      "name": "Charlie Magland"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/204tjrxf7ch9c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37693",
  "fulltext_url": null,
  "id": "204tjrxf7ch9c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.37693",
  "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.RT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.37693",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/204tjrxf7ch9c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.37693",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37693"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Cohomological change of coefficients for noncocommutative Hopf algebras",
  "title_text": "Cohomological change of coefficients for noncocommutative Hopf algebras",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/204tjrxf7ch9c",
  "venue": "arXiv",
  "versions": []
}