{"paper":{"title":"Simply transitive quaternionic lattices of rank 2 over F_q(t) and a non-classical fake quadric","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.NT"],"primary_cat":"math.GR","authors_text":"Alina Vdovina, Jakob Stix","submitted_at":"2013-04-19T21:09:54Z","abstract_excerpt":"We construct an infinite series of simply transitive irreducible lattices in PGL_2(F_q((t))) \\times PGL_2(F_q((t))) by means of a quaternion algebra over F_q(t). The lattices depend on an odd prime power q = p^r and a parameter \\tau\\ in F_q^* different from 1, and are the fundamental group of a square complex with just one vertex and universal covering T_{q+1} \\times T_{q+1}, a product of trees with constant valency q + 1.\n  Our lattices give rise via non-archimedian uniformization to smooth projective surfaces of general type over F_q((t)) with ample canonical class, Chern ratio (c_1)^2/c_2 ="},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5549","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"}