Title of article :
Quantum statistical mechanics over function fields Original Research Article
Author/Authors :
Caterina Consani ، نويسنده , , Matilde Marcolli، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2007
Abstract :
In this paper we construct a noncommutative space of “pointed Drinfeld modules” that generalizes to the case of function fields the noncommutative spaces of commensurability classes of image-lattices. It extends the usual moduli spaces of Drinfeld modules to possibly degenerate level structures. In the second part of the paper we develop some notions of quantum statistical mechanics in positive characteristic and we show that, in the case of Drinfeld modules of rank one, there is a natural time evolution on the associated noncommutative space, which is closely related to the positive characteristic L-functions introduced by Goss. The points of the usual moduli space of Drinfeld modules define KMS functionals for this time evolution. We also show that the scaling action on the dual system is induced by a Frobenius action, up to a Wick rotation to imaginary time.
Journal title :
Journal of Number Theory
Journal title :
Journal of Number Theory