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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 ="},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1304.5549","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-04-19T21:09:54Z","cross_cats_sorted":["math.AG","math.NT"],"title_canon_sha256":"75a1dbe4ee2481698bab61057ddf01db7238bab9e1fa4fcd9c4ebb4b425f66a6","abstract_canon_sha256":"3b7303f58c588b61e4966520558310e11bc65eef14c75c3e6b0c4196f9939b4a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:31.723778Z","signature_b64":"IAMAMO/jygAMm+FmAc9ehKUGa3OhKJ9xEsR+5mnlUpCh0/mU2AWmNn8tdXy9r6a3Vdk375xpg1ZobNaSNaS1Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f4a326fb17a5dd6f691c7de6282f8ca4dc01b786e8e4edb1c19457118ce1b65","last_reissued_at":"2026-05-18T03:27:31.723180Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:31.723180Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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). 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