{"paper":{"title":"Torsion in Rank-1 Drinfeld Modules and the Uniform Boundedness Conjecture","license":"","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Bjorn Poonen","submitted_at":"1995-07-06T00:00:00Z","abstract_excerpt":"It is conjectured that for fixed $A$, $r \\ge 1$, and $d \\ge 1$, there is a uniform bound on the size of the torsion submodule of a Drinfeld $A$-module of rank $r$ over a degree $d$ extension $L$ of the fraction field $K$ of $A$. We verify the conjecture for $r=1$, and more generally for Drinfeld modules having potential good reduction at some prime above a specified prime of $K$. Moreover, we show that within an $\\Lbar$-isomorphism class, there are only finitely many Drinfeld modules up to isomorphism over $L$ which have nonzero torsion. For the case $A=\\Fq[T]$, $r=1$, and $L=\\Fq(T)$, we give "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9507217","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"}