{"paper":{"title":"Change of coefficients in the $p \\neq \\ell$ local Langlands correspondence for $GL_n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.NT","authors_text":"Tibor Backhausz","submitted_at":"2018-12-11T03:42:18Z","abstract_excerpt":"Let $\\ell$ and $p$ be distinct primes, $n$ a positive integer, $F_\\ell$ an $\\ell$-adic local field of characteristic $0,$ and let $W(k)$ denote the ring of Witt vectors over an algebraically closed field of characteristic $p$. Work of Emerton-Helm, Helm and Helm-Moss defines and constructs a smooth $A[{GL}_n(F_\\ell)]$-module $\\tilde{\\pi}(\\rho_A)$ for a continuous Galois representation $\\rho_A : G_{F_\\ell} \\to {GL}_n(A)$ over a $p$-torsionfree reduced complete local $W(k)$-algebra $A$ interpolating the local Langlands correspondence. However, since $\\tilde{\\pi}$ is not a functor, there is no cl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.04208","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"}