Bost-Connes systems associated with function fields
Bost-Connes systems associated with function fields
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与功能域相关的 Bost-Connes 系统
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
Simen Rustad
中科院分区：
文献类型：
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作者：
S. Neshveyev;Simen Rustad
利用具有常数域F_q的整体函数域K、K中的有限素数集S和K的有限或无限的阿贝尔扩张L，我们将一个C ~*-动力系统联系起来。雅各布用德林费尔德模上的理想作用和康萨尼-马科利用K格的可积性定义的系统，或者至少是它们的基本群胚，与我们构造的特殊情况同构。我们证明了我们的系统的相变定理，并表明，唯一的KMS_对于每0<etale 1产生III型ITPFI因子_{q^{-eta n}}，其中n是F_q在L中的代数闭度.因此，对于n=+infty，我们得到类型III_0的因子。它的重量流是由Gal上的Frobenius元素平移的缩放悬浮流（ar F_q/F_q）。
With a global function field K with constant field F_q, a finite set S of primes in K and an abelian extension L of K, finite or infinite, we associate a C*-dynamical system. The systems, or at least their underlying groupoids, defined earlier by Jacob using the ideal action on Drinfeld modules and by Consani-Marcolli using commensurability of K-lattices are isomorphic to particular cases of our construction. We prove a phase transition theorem for our systems and show that the unique KMS_eta-state for every 0<etale1 gives rise to an ITPFI-factor of type III_{q^{-eta n}}, where n is the degree of the algebraic closure of F_q in L. Therefore for n=+infty we get a factor of type III_0. Its flow of weights is a scaled suspension flow of the translation by the Frobenius element on Gal(ar F_q/F_q).