{"paper":{"title":"A note on trace fields of complex hyperbolic groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Heleno Cunha, Nikolay Gusevskii","submitted_at":"2013-03-07T14:26:02Z","abstract_excerpt":"We show that if $\\Gamma$ is an irreducible subgroup of ${\\rm SU}(2,1)$, then $\\Gamma$ contains a loxodromic element $A$. If $A$ has eigenvalues $\\lambda_1 = \\lambda e^{i\\varphi},$ $\\lambda_2 = e^{-2i\\varphi}$, $\\lambda_3 = \\lambda^{-1}e^{i\\varphi}$, we prove that $\\Gamma$ is conjugate in ${\\rm SU}(2,1)$ to a subgroup of ${\\rm SU}(2,1,\\mathbb{Q}(\\Gamma,\\lambda)),$ where $\\mathbb{Q}(\\Gamma, \\lambda)$ is the field generated by the trace field $\\mathbb{Q}(\\Gamma)$ of $\\Gamma$ and $\\lambda$. It follows from this that if $\\Gamma$ is an irreducible subgroup of ${\\rm SU}(2,1)$ such that the trace fiel"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.1701","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"}