Journal of Noncommutative Geometry

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Volume 6, Issue 2, 2012, pp. 275–319
DOI: 10.4171/JNCG/92

Published online: 2012-04-16

On Bost–Connes type systems and complex multiplication

Bora Yalkinoglu[1]

(1) Université Paris VI, Paris

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. The abelian extensions obtained in this way are characterized by results of [Wei]. Our approach is based on a general construction of BC-type systems of Ha and Paugam [HP05] and extends the construction of the arithmetic subalgebra of Connes, Marcolli and Ramachandran [CMR05] for imaginary quadratic fields.

Keywords: Bost–Connes type systems, complex multiplication, Shimura varieties

Yalkinoglu Bora: On Bost–Connes type systems and complex multiplication. J. Noncommut. Geom. 6 (2012), 275-319. doi: 10.4171/JNCG/92