{"paper":{"title":"Torsion Points of order 2g+1 on odd degree hyperelliptic curves of genus g","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Boris M. Bekker, Yuri G. Zarhin","submitted_at":"2019-02-07T17:39:39Z","abstract_excerpt":"Let $K$ be an algebraically closed field of characteristic different from $2$, $g$ a positive integer, $f(x)\\in K[x]$ a degree $2g+1$ monic polynomial without repeated roots, $C_f: y^2=f(x)$ the corresponding genus g hyperelliptic curve over $K$, and $J$ the jacobian of $C_f$. We identify $C_f$ with the image of its canonical embedding into $J$ (the infinite point of $C_f$ goes to the zero of group law on $J$). It is known (arXiv:1809.03061 [math.AG]) that if $g>1$ then $C_f(K)$ does not contain torsion points, whose order lies between $3$ and $2g$.\n  In this paper we study torsion points of o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.02743","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"}