{"paper":{"title":"A new $\\operatorname{Gal}(\\overline{\\mathbb{Q}}/\\mathbb{Q})$-invariant of dessins d'enfants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Ravi Jagadeesan","submitted_at":"2014-03-30T01:55:41Z","abstract_excerpt":"We study the action of $\\operatorname{Gal}(\\overline{\\mathbb{Q}}/\\mathbb{Q})$ on the category of Belyi functions (finite, \\'{e}tale covers of $\\mathbb{P}^1_{\\overline{\\mathbb{Q}}}\\setminus \\{0,1,\\infty\\}$). We describe a new combinatorial $\\operatorname{Gal}(\\overline{\\mathbb{Q}}/\\mathbb{Q})$-invariant for whose monodromy cycle types above $0$ and $\\infty$ are the same. We use a version of our invariant to prove that $\\operatorname{Gal}(\\overline{\\mathbb{Q}}/\\mathbb{Q})$ acts faithfully on the set of Belyi functions whose monodromy cycle types above 0 and $\\infty$ are the same; the proof of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7690","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"}