KMS状态和复乘
KMS states and complex multiplication
摘要：
我们构造了一个量子统计力学系统，它将Bost-Connes系统推广到任意类数的虚二次域K，并充分结合了这类域的显式类域理论.该系统允许戴德金ζ函数作为分拆函数，Idele类群作为对称群.极端KMS状态在零温度interrupts这种对称性与伽罗瓦行动的算术子代数上的状态的值。我们也给出了原BC系统和GL（2）系统的Shimura簇的解释，这激发了虚二次域的构造。该构造的几何概念是K-格的可积性。
英文摘要：
We construct a quantum statistical mechanical system which generalizes the Bost-Connes system to imaginary quadratic fields K of arbitrary class number and fully incorporates the explict class field theory for such fields. This system admits the Dedekind zeta function as partition function and the Idele class group as group of symmetries. The extremal KMS states at zero temperature intertwine this symmetry with the Galois action on the values of the states on the arithmetic subalgebra. We also give an interpretation of the original BC system and of the GL(2) system in terms of Shimura varieties, which motivates the construction for imaginary quadratic fields. The geometric notion underlying the construction is that of commensurability of K-lattices.
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