Quantum statistical mechanics of the absolute Galois group

Manin, Yuri I.; Marcolli, Matilde

doi:10.3842/SIGMA.2020.038

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Quantum statistical mechanics of the absolute Galois group

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Manin, Yuri I.
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.3842/SIGMA.2020.038
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Citation

Manin, Y. I., & Marcolli, M. (2020). Quantum statistical mechanics of the absolute Galois group. Symmetry, Integrability and Geometry: Methods and Applications, 16: 038. doi:10.3842/SIGMA.2020.038.

Cite as: https://hdl.handle.net/21.11116/0000-0006-81BF-1

Abstract

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.