Noncommutative Geometry and Arithmetic
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Publication:3096685
zbMATH Open1234.46056arXiv1003.3662MaRDI QIDQ3096685
Publication date: 11 November 2011
Abstract: This is an overview of recent results aimed at developing a geometry of noncommutative tori with real multiplication, with the purpose of providing a parallel, for real quadratic fields, of the classical theory of elliptic curves with complex multiplication for imaginary quadratic fields. This talk concentrates on two main aspects: the relation of Stark numbers to the geometry of noncommutative tori with real multiplication, and the shadows of modular forms on the noncommutative boundary of modular curves, that is, the moduli space of noncommutative tori. To appear in Proc. ICM 2010.
Full work available at URL: https://arxiv.org/abs/1003.3662
real quadratic fieldsnoncommutative toriquantum statistical mechanicsreal multiplicationspectral triplesmodular shadowsnoncommutative boundary of modular curvesStark numbers
Noncommutative algebraic geometry (14A22) Noncommutative topology (46L85) Quantum dynamics and nonequilibrium statistical mechanics (general) (82C10) Noncommutative geometry (à la Connes) (58B34) Relations with noncommutative geometry (11M55)
Related Items (3)
Noncommutative calculus and the Gauss-Manin connection ⋮ Arithmetic Structures on Noncommutative Tori with Real Multiplication ⋮ Noncommutative geometry and arithmetics
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