{"paper":{"title":"On the density of rational points on rational elliptic surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Julie Desjardins","submitted_at":"2017-02-06T16:22:14Z","abstract_excerpt":"Let $\\mathscr{E}\\rightarrow\\mathbb{P}^1_\\mathbb{Q}$ be a non-trivial rational elliptic surface over $\\mathbb{Q}$ with base $\\mathbb{P}^1_\\mathbb{Q}$ (with a section). We conjecture that any non-trivial elliptic surface has a Zariski-dense set of $\\mathbb{Q}$-rational points. In this paper we work on solving the conjecture in case $\\mathscr{E}$ is rational by means of geometric and analytic methods. First, we show that for $\\mathscr{E}$ rational, the set $\\mathscr{E}(\\mathbb{Q})$ is Zariski-dense when $\\mathscr{E}$ is isotrivial with non-zero $j$-invariant and when $\\mathscr{E}$ is non-isotrivi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.01684","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"}