{
  "abstract": "Let $k$ be a field of characteristic $p>0$, $\\mathcal{F}$ a saturated fusion system over a finite $p$-group $P$, and $V$ an indecomposable capped endopermutation $kP$-module. Let $D_k^Ω(P)$ be the subgroup of the Dade group $D_k(P)$ generated by all the relative syzygies. It is known that $V$ has an endosplit $p$-permutation resolution if and only if the Dade class $[V]$ belongs to $D_k^Ω(P)$. We show that the resolution can be chosen to be $\\mathcal{F}$-stable if and only if $V$ is $\\mathcal{F}$-stable. As an application, we prove the following folklore result: if two blocks of finite groups are Morita equivalent via a bimodule with an endopermutation $kP$-source $V$ such that $[V]\\in D_k^Ω(P)$, then these two blocks are splendidly Rickard equivalent.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15971",
  "author_total": 1,
  "authors": [
    {
      "name": "Xin Huang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7s4vmsdgdfrkh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15971",
  "fulltext_url": null,
  "id": "7s4vmsdgdfrkh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15971",
  "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.GR"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7213238978",
  "pdf_url": "https://arxiv.org/pdf/2609.15971",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7s4vmsdgdfrkh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.15971",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15971"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Fusion-stable endosplit $p$-permutation resolutions",
  "title_text": "Fusion-stable endosplit p-permutation resolutions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/7s4vmsdgdfrkh",
  "venue": "arXiv",
  "versions": []
}