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

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dc.creatorHa, Eugene
dc.creatorPaugam, Frederic
dc.date2005-07-05
dc.date.accessioned2026-07-07T05:21:25Z
dc.date.available2026-07-07T05:21:25Z
dc.descriptionWe construct a quantum statistical mechanical system $(A,s)$ analogous to the systems constructed by Bost-Connes and Connes-Marcolli in the case of Shimura varieties. Along the way, we define a new Bost-Connes system for number fields which has the ``correct'' partition function and the ``correct'' symmetries. 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 exhibit phase transitions with spontaneous symmetry breaking, and to classify their KMS states, at least for low temperature.
dc.description37 pages, LaTeX
dc.identifierhttps://arxiv.org/abs/math/0507101
dc.identifierhttp://arxiv.org/abs/math/0507101
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75685
dc.subjectOperator Algebras
dc.subjectMathematical Physics
dc.subjectNumber Theory
dc.subject58B34, 46L55, 11F03, 11G18, 11M06, 82B26, 82B10
dc.titleBost-Connes-Marcolli systems for Shimura varieties. I. Definitions and formal analytic properties
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