{"paper":{"title":"Weak Approximation over Function Fields of Curves over Large or Finite Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Yong Hu","submitted_at":"2009-07-15T08:44:56Z","abstract_excerpt":"Let $K=k(C)$ be the function field of a curve over a field $k$ and let $X$ be a smooth, projective, separably rationally connected $K$-variety with $X(K)\\neq\\emptyset$. Under the assumption that $X$ admits a smooth projective model $\\pi: \\mathcal{X}\\to C$, we prove the following weak approximation results: (1) if $k$ is a large field, then $X(K)$ is Zariski dense; (2) if $k$ is an infinite algebraic extension of a finite field, then $X$ satisfies weak approximation at places of good reduction; (3) if $k$ is a nonarchimedean local field and $R$-equivalence is trivial on one of the fibers $\\math"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.2529","kind":"arxiv","version":4},"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"}