{
  "abstract": "Let F be a field, G = GL_n(F), and let St be the Steinberg module of G. For a parabolic subgroup P of G, let St_P be its Steinberg module. There is a natural map rho_P: St -> St_P corresponding to intersection of a modular symbol with the Borel--Serre boundary. We construct a ZP-resolution Sh_P of St_P, the P-sharbly resolution. We also construct a P-equivariant chain map from the sharbly resolution of St to the P-sharbly resolution of St_P which enables us to compute the map induced on Steinberg homologies by rho_P. In the case when F is a number field and Gamma subset G is a torsion-free arithmetic subgroup, rho_P induces the restriction map H^(Gamma, E) -> H^(Gamma cap P, E) via Borel--Serre duality, for any coefficient module E which is flat over the base ring. If E is a vector space over Z/pZ this provides a computation of the restriction map on cohomology from Gamma to Gamma cap P in terms of sharblies, which enables the study of this restriction map in characteristic p, where Eisenstein series cannot be used.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03303",
  "author_total": 2,
  "authors": [
    {
      "name": "Avner Ash"
    },
    {
      "name": "Paul E. Gunnells"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bmnmypwy92fx6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03303",
  "fulltext_url": null,
  "id": "bmnmypwy92fx6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03303",
  "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.NT"
    ],
    [
      "arxiv",
      "math.RT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.03303",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bmnmypwy92fx6.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:14Z",
      "native_id": "2611.03303",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03303"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A resolution of the Steinberg module of a parabolic subgroup of GL_n",
  "title_text": "A resolution of the Steinberg module of a parabolic subgroup of GL_n",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:28Z",
  "url": "https://research.draconitic.com/paper/bmnmypwy92fx6",
  "venue": "arXiv",
  "versions": []
}