{"paper":{"title":"Automorphy of Symm^5(GL(2)) and base change","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Luis V. Dieulefait","submitted_at":"2012-08-20T08:50:11Z","abstract_excerpt":"We prove that for any Hecke eigenform f of level 1 and arbitrary weight there is a self-dual cuspidal automorphic form $\\pi$ of $GL_6(\\Q)$ corresponding to $\\Symm^5 (f)$, i.e., such that the system of Galois representations attached to $\\pi$ agrees with the 5-th symmetric power of the one attached to f. We also improve the base change result that we obtained in a previous work: for any newform f, and any totally real number field F (no extra assumptions on f or F), we prove the existence of base change relative to the extension $F/\\Q$. Finally, we combine the previous results to deduce that ba"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3946","kind":"arxiv","version":3},"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"}