{"paper":{"title":"Conductors and minimal discriminants of hyperelliptic curves with rational Weierstrass points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Padmavathi Srinivasan","submitted_at":"2015-08-21T04:09:47Z","abstract_excerpt":"Let $C$ be a hyperelliptic curve of genus $g$ over the fraction field $K$ of a discrete valuation ring $R$. Assume that the residue field $k$ of $R$ is perfect and that $\\mathop{\\textrm{char}} k \\neq 2$. Assume that the Weierstrass points of $C$ are $K$-rational. Let $S = \\mathop{\\textrm{Spec}} R$. Let $\\mathcal{X}$ be the minimal proper regular model of $C$ over $S$. Let $\\mathop{\\textrm{Art}} (\\mathcal{X}/S)$ denote the Artin conductor of the $S$-scheme $\\mathcal{X}$ and let $\\nu (\\Delta)$ denote the minimal discriminant of $C$. We prove that $-\\mathop{\\textrm{Art}} (\\mathcal{X}/S) \\leq \\nu "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.05172","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"}