On Bost-Connes type systems and Complex Multiplication
Bora Yalkinoglu
TL;DR
This paper extends the construction of Bost-Connes type systems to general number fields with CM by leveraging the theory of Complex Multiplication for Siegel modular varieties, broadening the scope beyond imaginary quadratic fields.
Contribution
It introduces a new method to construct arithmetic subalgebras for BC-type systems associated with CM fields using advanced CM theory for Siegel modular varieties.
Findings
Constructed arithmetic subalgebras for BC-type systems in broader CM field contexts.
Extended previous work from imaginary quadratic fields to general CM fields.
Provided a new framework connecting CM theory and quantum statistical mechanics.
Abstract
By using the theory of Complex Multiplication for general Siegel modular varieties we construct arithmetic subalgebras for BC-type systems attached to number fields containing a CM field. Our approach extends the construction of Connes, Marcolli and Ramachandran given in the case of imaginary quadratic fields.
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