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Published May 5, 2020 | Accepted Version + Published
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Quantum Statistical Mechanics of the Absolute Galois Group

Manin, Yuri I.
Marcolli, Matilde ORCID icon
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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.

Additional Information

© 2020 The Author(s) under the terms of the Creative Commons Attribution-ShareAlike License. Received August 01, 2019, in final form April 15, 2020; Published online May 05, 2020. This paper is a contribution to the Special Issue on Integrability, Geometry, Moduli in honor of Motohico Mulase for his 65th birthday. The full collection is available at https://www.emis.de/journals/SIGMA/Mulase.html. The second named author is partially supported by NSF grant DMS-1707882, and by NSERC Discovery Grant RGPIN-2018-04937 and Accelerator Supplement grant RGPAS-2018-522593. We thank the anonymous referees for several very useful comments that significantly improve the paper, and Lieven Le Bruyn for his suggestions in a series of mails that helped us to avoid ambiguities.

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Published - sigma20-038.pdf

Accepted Version - 1907.13545.pdf

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