A classification of C -Fuchsian subgroups of Picard modular groups

• Jouni Parkkonen ^[1] ; Frédéric Paulin ^[2]
  1. [1] University of Jyväskylä

     University of Jyväskylä

     Jyväskylä, Finlandia

     
  2. [2] University of Paris-Saclay

     University of Paris-Saclay

     Arrondissement de Palaiseau, Francia

     
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 121, Nº 1, 2017, págs. 57-74
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • Given an imaginary quadratic extension K of Q, we give a classification of the maximal nonelementary subgroups of the Picard modular group PSU1,2(OK) preserving a complex geodesic in the complex hyperbolic plane H2C. Complementing work of Holzapfel, Chinburg-Stover and M\"oller-Toledo, we show that these maximal C-Fuchsian subgroups are arithmetic, arising from a quaternion algebra (D,DKQ) for some explicit D∈N−{0} and DK the discriminant of K. We thus prove the existence of infinitely many orbits of K-arithmetic chains in the hypersphere of P2(C)