{
  "abstract": "Let $G$ be a quasi-split $p$-adic group, defined over a non-archimedean local field of residue cardinality $q$, and $R$ be a $\\mathbb{Z}[\\sqrt{q}^{-1},μ_{4p^\\infty}]$-algebra. We generalize the constructions of Shahidi local coefficients and Langlands-Shahidi gamma factors to the setting of co-Whittaker $R$-representations. For classical $p$-adic groups, we prove there is a unique integral morphism of endomorphism rings of Gelfand--Graev representations, interpolating the (standard) local generic transfer to a general linear group. This yields a local transfer morphism in families, which allows us to deduce properties of the local $\\ell$-adic generic transfer and congruences modulo primes $\\ell\\neq p$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31615",
  "author_total": 2,
  "authors": [
    {
      "name": "Johannes Girsch"
    },
    {
      "name": "Robert Kurinczuk"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/798v9wgxmfe0v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31615",
  "fulltext_url": null,
  "id": "798v9wgxmfe0v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31615",
  "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.NT"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7223386551",
  "pdf_url": "https://arxiv.org/pdf/2610.31615",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/798v9wgxmfe0v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.31615",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31615"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Langlands-Shahidi gamma factors and local transfer in families",
  "title_text": "Langlands-Shahidi gamma factors and local transfer in families",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/798v9wgxmfe0v",
  "venue": "arXiv",
  "versions": []
}