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Reconstructing global fields from dynamics in the abelianized Galois group

Cornelissen, Gunther and Li, Xin and Marcolli, Matilde and Smit, Harry (2019) Reconstructing global fields from dynamics in the abelianized Galois group. Selecta Mathematica - New Series, 25 (6). Art. No. 24. ISSN 1022-1824 .

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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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Additional Information:© The Author(s) 2019. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. First Online 15 March 2019. 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).
Subject Keywords:Class field theory; Bost–Connes system; Anabelian geometry; Neukirch–Uchida theorem; L-series
Classification Code:2010 Mathematics Subject Classification: 11M55; 11R37; 11R42; 11R56; 14H30; 46N55; 58B34; 82C10
Record Number:CaltechAUTHORS:20170712-082102987
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Official Citation:Cornelissen, G., Li, X., Marcolli, M. et al. Sel. Math. New Ser. (2019) 25: 24.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78985
Deposited By: Tony Diaz
Deposited On:12 Jul 2017 17:16
Last Modified:15 Mar 2019 16:52

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