Fun with F1

JOURNAL OF NUMBER THEORY

卷:129

Article

Connes, Alain^2,3,4  Consani, Caterina¹  Marcolli, Matilde^5,6 

[1] Johns Hopkins Univ, Dept Math, Baltimore, MD 21218 USA

[2] Coll France, F-75005 Paris, France

[3] IHES, Bures Sur Yvette, France

[4] Vanderbilt Univ, Nashville, TN USA

[5] Max Planck Inst Math, D-53111 Bonn, Germany

[6] CALTECH, Dept Math, Pasadena, CA 91125 USA

关键词: BC-system;    Endomotives;    Varieties over F-1;    Frobenius correspondence;   

DOI  :  10.1016/j.jnt.2008.08.007

来源: Elsevier

【 摘 要 】

Text. We show that the algebra and the endomotive of the quantum statistical mechanical system of Bost-Connes naturally arises by extension of scalars from the field with one element to rational numbers. The inductive structure of the abelian part of the endomotive corresponds to the tower of finite extensions of that field, while the endomorphisms reflect the Frobenius correspondences. This gives in particular an explicit model over the integers for this endomotive, which is related to the original Hecke algebra description. We study the reduction at a prime of the endomotive and of the corresponding noncommutative crossed product algebra. Video. For a video summary of this paper, please visit http://www.youtube.com/watch?v=az_0pxm1jrl. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

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