{
  "abstract": "We prove that every finite symmetric tensor category over an algebraically closed field of positive characteristic admits a symmetric tensor functor to a higher Verlinde category. This was conjectured for arbitrary symmetric tensor categories of moderate growth by Benson, Etingof and Ostrik. The proof uses higher Frobenius functors, introduced by the authors in [CF1]. The main effort is directed towards a proof of a conjecture from [CF1] about thick tensor ideals in the representation category of elementary abelian $p$-groups, which implies that the higher Frobenius functors are symmetric monoidal. In fact, we prove a refinement of the latter conjecture that relates tensoring with restricted Steinberg modules to an iterated generalised cohomology of modules of elementary abelian $p$-groups.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04096",
  "author_total": 2,
  "authors": [
    {
      "name": "Kevin Coulembier"
    },
    {
      "name": "Johannes Flake"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4h7n9j8j8n8k9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04096",
  "fulltext_url": null,
  "id": "4h7n9j8j8n8k9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04096",
  "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.CT"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7220705236",
  "pdf_url": "https://arxiv.org/pdf/2610.04096",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4h7n9j8j8n8k9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.04096",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04096"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The Benson--Etingof--Ostrik conjecture for finite tensor categories",
  "title_text": "The Benson--Etingof--Ostrik conjecture for finite tensor categories",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/4h7n9j8j8n8k9",
  "venue": "arXiv",
  "versions": []
}