2006/07/15 by Caterina Consani, Matilde Marcolli, Consani, Caterina +1
Mathematics · #11G09 #58B34 #82A15 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Mathematical Analysis and Transform Methods #Number Theory (math.NT) #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.math/0607363
openalex publication_date 2006/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Q-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.