{"paper":{"title":"Examples of character varieties in characteristic $p$ and ramification","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Joan Porti, Luisa Paoluzzi","submitted_at":"2019-05-17T11:06:52Z","abstract_excerpt":"We study $\\mathrm{SL}_2(\\mathbb{F})$-character varieties of knots over algebraically closed fields $\\mathbb{F}$. We give a sufficient condition in terms of the double branched cover of a $2$-bridge knot (or, equivalently, of its Alexander polynomial) on the characteristic of $\\mathbb{F}$, an odd prime, for the $\\mathrm{SL}_2(\\mathbb{F})$-character variety to present ramification phenomena. Finally we provide several explicit computations of character varieties to illustrate the result, exhibiting also other types of ramification."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.07196","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"}