{
  "abstract": "We state a conjecture, local Langlands in families , connecting the centre of the category of smooth representations on Z ⁢ [ q − 1 ] \\mathbb{Z}[\\sqrt{q}^{-1}] -modules of a quasi-split 𝑝-adic group G \\mathrm{G} (where 𝑞 is the cardinality of the residue field of the underlying local field), the ring of global functions on the stack of Langlands parameters for G \\mathrm{G} over Z ⁢ [ q − 1 ] \\mathbb{Z}[\\sqrt{q}^{-1}] , and the endomorphisms of a Gelfand–Graev representation for G \\mathrm{G} . For a class of classical 𝑝-adic groups (symplectic, unitary, or odd special orthogonal groups), we prove this conjecture after inverting an integer depending only on G \\mathrm{G} . Along the way, we show that the local Langlands correspondence for classical 𝑝-adic groups (1) preserves integrality of ℓ-adic representations, (2) satisfies an “extended” (generic) packet conjecture, (3) is compatible with parabolic induction up to semisimplification (generalizing a result of Moussaoui), hence induces a semisimple local Langlands correspondence, and (4) the semisimple correspondence is compatible with automorphisms of ℂ fixing q \\sqrt{q} .",
  "abstract_shown": true,
  "affiliations": [
    "IMJ-PRG , Sorbonne Université , Université Paris Cité, CNRS, 4 Place Jussieu, 75005 , Paris , France",
    "Department of Mathematics , Imperial College , London , SW7 2AZ , United Kingdom",
    "School of Mathematics and Statistics , University of Sheffield , Sheffield , S3 7RH , United Kingdom",
    "Department of Mathematics & Statistics , University of Maine , 5752 Neville Hall , Orono , ME 04469 , USA"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 4,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Jean-François Dat",
      "orcid": "0000-0002-6411-3990"
    },
    {
      "affs": [
        1
      ],
      "name": "David Helm",
      "orcid": "0009-0001-4820-9941"
    },
    {
      "affs": [
        2
      ],
      "name": "Robert Kurinczuk",
      "orcid": "0000-0002-9356-4563"
    },
    {
      "affs": [
        3
      ],
      "name": "Gilbert Moss",
      "orcid": "0000-0001-9841-2406"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/18nb640bcj2y4.bib",
  "cited_by": 17,
  "doi": "10.1515/crelle-2026-0034",
  "fulltext_url": null,
  "id": "18nb640bcj2y4",
  "issns": [
    "0075-4102",
    "1435-5345"
  ],
  "landing_url": "https://doi.org/10.1515/crelle-2026-0034",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2602|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W4399695780",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-05-20",
  "publisher": "De Gruyter",
  "ris": "https://research.draconitic.com/paper/18nb640bcj2y4.ris",
  "sources": [
    {
      "first_seen": "2026-11-08T13:20:35Z",
      "native_id": "W4399695780",
      "source": "openalex",
      "url": "https://doi.org/10.1515/crelle-2026-0034"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2602|Advanced Algebra and Geometry",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Local Langlands in families: The banal case",
  "title_text": "Local Langlands in families: The banal case",
  "type": "peer-reviewed",
  "updated_at": "2026-11-09T13:20:59Z",
  "url": "https://research.draconitic.com/paper/18nb640bcj2y4",
  "venue": "Journal für die reine und angewandte Mathematik (Crelles Journal)",
  "versions": []
}