{"paper":{"title":"A classification of $\\mathbb C$-Fuchsian subgroups of Picard modular groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.NT","authors_text":"Fr\\'ed\\'eric Paulin, Jouni Parkkonen","submitted_at":"2015-03-19T15:32:47Z","abstract_excerpt":"Given an imaginary quadratic extension $K$ of $\\mathbb Q$, we give a classification of the maximal nonelementary subgroups of the Picard modular group $\\operatorname{PSU}_{1,2}(\\mathcal O_K)$ preserving a complex geodesic in the complex hyperbolic plane $\\mathbb H^2_\\mathbb C$. Complementing work of Holzapfel, Chinburg-Stover and M\\\"oller-Toledo, we show that these maximal $\\mathbb C$-Fuchsian subgroups are arithmetic, arising from a quaternion algebra $\\Big(\\!\\begin{array}{c} D\\,,D_K\\\\\\hline\\mathbb QQ\\end{array} \\!\\Big)$ for some explicit $D\\in\\mathbb N-\\{0\\}$ and $D_K$ the discriminant of $K"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05801","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"}