Abstract
We study a dynamical system induced by the Artin reciprocity map for a global field. We translate the conjugacy of such dynamical systems into various arithmetical properties that are equivalent to field isomorphism, relating it to anabelian geometry.
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This paper supersedes [5], of which it is the second (and final) part, dealing with the dynamical systems aspects of the theory. The first part [6] dealt with physics aspects related to partition functions, and [8] is a companion paper, only containing number theoretical results. Part of this work was done whilst the first two authors enjoyed the hospitality of the University of Warwick (special thanks to Richard Sharp for making it possible)
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Cornelissen, G., Li, X., Marcolli, M. et al. Reconstructing global fields from dynamics in the abelianized Galois group. Sel. Math. New Ser. 25, 24 (2019). https://doi.org/10.1007/s00029-019-0469-8
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DOI: https://doi.org/10.1007/s00029-019-0469-8