{"paper":{"title":"On Fields of rationality for automorphic representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Nicolas Templier, Sug Woo Shin","submitted_at":"2013-02-25T16:42:31Z","abstract_excerpt":"This paper proves two results on the field of rationality $\\Q(\\pi)$ for an automorphic representation $\\pi$, which is the subfield of $\\C$ fixed under the subgroup of $\\Aut(\\C)$ stabilizing the isomorphism class of the finite part of $\\pi$. For general linear groups and classical groups, our first main result is the finiteness of the set of discrete automorphic representations $\\pi$ such that $\\pi$ is unramified away from a fixed finite set of places, $\\pi_\\infty$ has a fixed infinitesimal character, and $[\\Q(\\pi):\\Q]$ is bounded. The second main result is that for classical groups, $[\\Q(\\pi):"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.6144","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":""},"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"}