{"paper":{"title":"An abelian subfield of the dyadic division field of a hyperelliptic Jacobian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jeffrey Yelton","submitted_at":"2018-02-28T16:10:35Z","abstract_excerpt":"Given a field $k$ of characteristic different from $2$ and an integer $d \\geq 3$, let $J$ be the Jacobian of the \"generic\" hyperelliptic curve given by $y^2 = \\prod_{i = 1}^d (x - \\alpha_i)$, where the $\\alpha_i$'s are transcendental and independent over $k$; it is defined over the transcendental extension $K / k$ generated by the symmetric functions of the $\\alpha_i$'s. We investigate certain subfields of the field $K_{\\infty}$ obtained by adjoining all points of $2$-power order of $J(\\bar{K})$. In particular, we explicitly describe the maximal abelian subextension of $K_{\\infty} / K(J[2])$ a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.10504","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"}