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Quantum Statistical Mechanics of the Absolute Galois Group

2020
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Symmetry, Integrability and Geometry: Methods and Applications
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We present possible extensions of the quantum statistical mechanical formulation of class field theory to the non-abelian case, based on the action of the absolute Galois group on Grothendieck's dessins d'enfant, the embedding in the Grothendieck-Teichmüller group, and the Drinfeld-Ihara involution. An interested reader will find much more details and basic references in [21, Chapter 3, Section 2]. This construction of the Bost-Connes system was then generalized in [22, 36, 46, 63] , to the

doi:10.3842/sigma.2020.038
fatcat:qbibph6e2nfb3f6d6nt7zk6344