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International Mathematics Research Papers (2005) 2005:237-286, doi:10.1155/IMRP.2005.237
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Copyright © 2005 Hindawi Publishing Corporation. All rights reserved.

Bost-Connes-Marcolli systems for Shimura varieties. Part I. Definitions and formal analytic properties

Eugene Ha and Frédéric Paugam

We construct a quantum statistical mechanical system Formula analogous to the Connes-Marcolli system in the case of Shimura varieties. Along the way, we define a new Bost-Connes system for number fields which has the "correct" symmetries andthe "correct" partition function. We give a formalism that applies to general Shimura data Formula. The object of this series of papers is to show that these systems have phase transitions and spontaneous symmetry breaking, and to classify their KMS states, at least for low temperature.


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