{"paper":{"title":"Local Langlands in families: The banal case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.RT","authors_text":"David Helm, Gilbert Moss, Jean-Fran\\c{c}ois Dat, Robert Kurinczuk","submitted_at":"2024-06-13T16:22:40Z","abstract_excerpt":"We state a conjecture, local Langlands in families, connecting the centre of the category of smooth representations on $\\mathbb{Z}[\\sqrt{q}^{-1}]$-modules of a quasi-split $p$-adic group $\\mathrm{G}$ (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 $\\mathrm{G}$ over $\\mathbb{Z}[\\sqrt{q}^{-1}]$, and the endomorphisms of a Gelfand-Graev representation for $\\mathrm{G}$. For a class of classical $p$-adic groups (symplectic, unitary, or split odd special orthogonal groups), we prove this conjectu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.09283","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2406.09283/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}