{"paper":{"title":"Torsion points in families of Drinfeld modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Dragos Ghioca, Liang-Chung Hsia","submitted_at":"2012-06-29T15:07:58Z","abstract_excerpt":"Let $\\Phi^\\l$ be an algebraic family of Drinfeld modules defined over a field $K$ of characteristic $p$, and let $\\bfa,\\bfb\\in K[\\l]$. Assume that neither $\\bfa(\\l)$ nor $\\bfb(\\l)$ is a torsion point for $\\Phi^\\l$ for all $\\l$. If there exist infinitely many $\\l\\in\\Kbar$ such that both $\\bfa(\\l)$ and $\\bfb(\\l)$ are torsion points for $\\Phi^\\l$, then we show that for each $\\l\\in\\Kbar$, we have that $\\bfa(\\l)$ is torsion for $\\Phi^\\l$ if and only if $\\bfb(\\l)$ is torsion for $\\Phi^\\l$. In the case $\\bfa,\\bfb\\in K$, then we prove in addition that $\\bfa$ and $\\bfb$ must be $\\Fpbar$-linearly depend"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.7047","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"}