{"paper":{"title":"On the automorphisms of the non-split Cartan modular curves of prime level","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Valerio Dose","submitted_at":"2015-03-17T18:55:56Z","abstract_excerpt":"We study the automorphisms of the non-split Cartan modular curves $X_{ns}(p)$ of prime level $p$. We prove that if $p\\geq 37$ all the automorphisms preserve the cusps. Furthermore, if $p\\equiv 1\\text{ mod }12$ and $p\\neq 13$, the automorphism group is generated by the modular involution given by the normalizer of a non-split Cartan subgroup of $\\text{GL}_2(\\mathbb F_p)$. We also prove that for every $p\\geq 37$ such that $X_{ns}(p)$ has a CM rational point, the existence of an exceptional rational automorphism would give rise to an exceptional rational point on the modular curve $X_{ns}^+(p)$ a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05165","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"}