{"paper":{"title":"P-torsion monodromy representations of elliptic curves over geometric function fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Benjamin Bakker, Jacob Tsimerman","submitted_at":"2014-03-27T18:46:06Z","abstract_excerpt":"Given a complex quasiprojective curve $B$ and a non-isotrivial family $\\mathcal{E}$ of elliptic curves over $B$, the $p$-torsion $\\mathcal{E}[p]$ yields a monodromy representation $\\rho_\\mathcal{E}[p]:\\pi_1(B)\\rightarrow \\mathrm{GL}_2(\\mathbb{F}_p)$. We prove that if $\\rho_{\\mathcal E}[p]\\cong \\rho_{\\mathcal E'}[p]$ then $\\mathcal{E}$ and $\\mathcal E'$ are isogenous, provided $p$ is larger than a constant depending only on the gonality of $B$. This can be viewed as a function field analog of the Frey--Mazur conjecture, which states that an elliptic curve over $\\mathbb{Q}$ is determined up to i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7168","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"}