Bost-connes-marcolli Systems for Shimura Varieties. I. Definitions and Formal Analytic Properties

@inproceedings{HaBostconnesmarcolliSF,
  title={Bost-connes-marcolli Systems for Shimura Varieties. I. Definitions and Formal Analytic Properties},
  author={Eugene Ha and Fr{\'e}d{\'e}ric Paugam}
}
We construct a Quantum Statistical Mechanical system (A, σ t) analogous to the Bost-Connes-Marcolli system of [CM04] in the case of Shimura varieties. Along the way, we define a new Bost-Connes system for number fields which has the " correct " symmetries and the " correct " partition function. We give a formalism that applies to general Shimura data (G, X). The object of this series of papers is to show that these systems have phase transitions and spontaneous symmetry breaking, and to… CONTINUE READING
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