{"paper":{"title":"Canonical models of arithmetic $(1; \\infty)$ curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Jeroen Sijsling","submitted_at":"2017-07-04T21:30:37Z","abstract_excerpt":"In 1983 Takeuchi showed that up to conjugation there are exactly 4 arithmetic subgroups of $\\textrm{PSL}_2 (\\mathbb{R})$ with signature $(1; \\infty)$. Shinichi Mochizuki gave a purely geometric characterization of the corresponding arithmetic $(1; \\infty)$-curves, which also arise naturally in the context of his recent work on inter-universal Teichm\\\"uller theory.\n  Using Bely\\u{\\i} maps, we explicitly determine the canonical models of these curves. We also study their arithmetic properties and modular interpretations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.01158","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"}