{"paper":{"title":"Some cases of Serre's uniformity problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Pedro Lemos","submitted_at":"2018-08-09T12:23:17Z","abstract_excerpt":"We show that if $E/\\mathbb{Q}$ is an elliptic curve without complex multiplication and for which there is a prime $q$ such that the image of $\\bar{\\rho}_{E,q}$ is contained in the normaliser of a split Cartan subgroup of $\\rm{GL}_2(\\mathbb{F}_q)$, then $\\bar{\\rho}_{E,p}$ surjects onto $\\rm{GL}_2(\\mathbb{F}_p)$ for every prime $p>37$. This result complements a previous result by the author. We also prove analogue results for certain families of $\\mathbb{Q}$-curves, building on results of Ellenberg (2004) and Le Fourn (2016)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.03110","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"}