{"paper":{"title":"Quadratic Chabauty for Modular Curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Samir Siksek","submitted_at":"2017-04-03T08:44:50Z","abstract_excerpt":"Let $X/\\mathbb{Q}$ be a curve of genus $g \\ge 2$ with Jacobian $J$ and let $\\ell$ be a prime of good reduction. Using Selmer varieties, Kim defines a decreasing sequence \\[ X(\\mathbb{Q}_\\ell) \\supseteq X(\\mathbb{Q}_\\ell)_1 \\supseteq X(\\mathbb{Q}_\\ell)_2 \\supseteq \\cdots \\] all containing the rational points of $X$. Thanks to the work of Coleman, the `Chabauty set' $X(\\mathbb{Q}_\\ell)_1$ is known to be finite provided the Mordell--Weil rank of $J$ is smaller than $g$. In this case one has a practical strategy that often succeeds in computing the set of rational points of $X$. Balakrishnan and D"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.00473","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"}