{"paper":{"title":"The local Langlands correspondence in families and Ihara's lemma for U(n)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Claus Sorensen","submitted_at":"2014-06-06T22:33:46Z","abstract_excerpt":"The goal of this paper is to reformulate the conjectural \"Ihara lemma\" for $U(n)$ in terms of the local Langlands correspondence in families $\\tilde{\\pi}_{\\Sigma}(\\cdot)$, as currently being developed by Emerton and Helm. The reformulation roughly takes the following form. Suppose we are given an irreducible mod $\\ell$ Galois representation $\\bar{r}$, which is modular of full level (and small weight), and a finite set of places $\\Sigma$ -- none of which divide $\\ell$. Then $\\tilde{\\pi}_{\\Sigma}(r)$ exists, and has a global realization as a natural module of algebraic modular forms, where $r$ i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.1830","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}