Quantum Statistical Mechanics of the Absolute Galois Group

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2020
• Main Authors: Manin, Yuri I., Marcolli, Matilde
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2020
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/210712
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Quantum Statistical Mechanics of the Absolute Galois Group. Yuri I. Manin and Matilde Marcolli. SIGMA 16 (2020), 038, 52 pages

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 i...