KMS states and complex multiplication

• Alain Connes ^[1] ; Matilde Marcolli ^[2] ; Niranjan Ramachandran ^[3]
  1. [1] Collège de France

     Collège de France

     París, Francia

     
  2. [2] Max-Planck Institut für Mathematik, Alemania
  3. [3] Department of Mathematics, University of Maryland, USA

  Mostrar afiliaciones +
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 11, Nº. 3-4, 2006, págs. 325-347
• Idioma: inglés
• Enlaces
  • Texto completo (pdf)
• Resumen

  • We construct a quantum statistical mechanical system which generalizes the Bost–Connes system to imaginary quadratic fields K of arbitrary class number and fully incorporates the explicit class field theory for such fields. This system admits the Dedekind zeta function as partition function and the idèle class group as group of symmetries. The extremal KMS states at zero temperature intertwine this symmetry with the Galois action on the values of the states on the arithmetic subalgebra. The geometric notion underlying the construction is that of commensurability of K-lattices.