{
  "abstract": "We prove the Díaz$\\unicode[Arial]{x2013}$Park conjecture for sharpness of saturated fusion systems. More generally, for every saturated fusion system $\\mathcal F$ over a finite $p$-group and every Mackey functor for $\\mathcal F$ over the localisation $\\mathbb{Z}_{(p)}$ of the integers at $p$, the higher limits of its contravariant part over the centric orbit category vanish in all positive degrees. In particular, the subgroup and normaliser decompositions of every $p$-local finite group $(S,\\mathcal F,\\mathcal L)$ over the $\\mathcal F$-centric subgroups are sharp. This answers in the affirmative a question in the list of important open problems in [M. Aschbacher, R. Kessar and B. Oliver, Fusion Systems in Algebra and Topology, Cambridge Univ. Press (2011)], and proves the sharpness conjecture stated in [M. Aschbacher and B. Oliver, Fusion systems, Bull. Amer. Math. Soc. (2016)] and Conjecture 1.2 of [E. Yalç$\\unicode[Arial]{x131}$n, Higher limits over the fusion orbit category, Adv. Math. (2022)]. The proof is algebraic and does not rely on the classification of finite simple groups.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02043",
  "author_total": 2,
  "authors": [
    {
      "name": "Baoyu Zhang"
    },
    {
      "name": "Shengmin Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/04yhznmg9yfgb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02043",
  "fulltext_url": null,
  "id": "04yhznmg9yfgb",
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  "landing_url": "https://arxiv.org/abs/2611.02043",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AT"
    ],
    [
      "arxiv",
      "math.CT"
    ],
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      "arxiv",
      "math.GR"
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      "arxiv",
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  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02043",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/04yhznmg9yfgb.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.02043",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02043"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A proof of the sharpness conjectures for all saturated fusion systems",
  "title_text": "A proof of the sharpness conjectures for all saturated fusion systems",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/04yhznmg9yfgb",
  "venue": "arXiv",
  "versions": []
}