Inventiones mathematicae

, Volume 191, Issue 2, pp 383–425 | Cite as

On arithmetic models and functoriality of Bost-Connes systems. With an appendix by Sergey Neshveyev

  • Bora YalkinogluEmail author


This paper has two parts. In the first part we construct arithmetic models of Bost-Connes systems for arbitrary number fields, which has been an open problem since the seminal work of Bost and Connes (Sel. Math. 1(3):411–457, 1995). In particular our construction shows how the class field theory of an arbitrary number field can be realized through the dynamics of a certain operator algebra. This is achieved by working in the framework of Endomotives, introduced by Connes, Consani and Marcolli (Adv. Math. 214(2):761–831, 2007), and using a classification result of Borger and de Smit (arXiv:1105.4662) for certain Λ-rings in terms of the Deligne-Ribet monoid. Moreover the uniqueness of the arithmetic model is shown by Sergey Neshveyev in an appendix. In the second part of the paper we introduce a base-change functor for a class of algebraic endomotives and construct in this way an algebraic refinement of a functor from the category of number fields to the category of Bost-Connes systems, constructed recently by Laca, Neshveyev and Trifkovic (arXiv:1010.4766).

Mathematics Subject Classification

11R37 11R20 11M55 58B34 46L55 


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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Max-Planck Institute for MathematicsBonnGermany

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