Selecta Mathematica

, 25:24 | Cite as

Reconstructing global fields from dynamics in the abelianized Galois group

  • Gunther CornelissenEmail author
  • Xin Li
  • Matilde Marcolli
  • Harry Smit
Open Access


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.


Class field theory Bost–Connes system Anabelian geometry Neukirch–Uchida theorem L-series 

Mathematics Subject Classification

11M55 11R37 11R42 11R56 14H30 46N55 58B34 82C10 



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© The Author(s) 2019

Open AccessThis 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.

Authors and Affiliations

  • Gunther Cornelissen
    • 1
    Email author
  • Xin Li
    • 2
  • Matilde Marcolli
    • 3
    • 4
    • 5
  • Harry Smit
    • 1
  1. 1.Mathematisch InstituutUniversiteit UtrechtUtrechtNetherlands
  2. 2.School of Mathematical SciencesQueen Mary University of LondonLondonUK
  3. 3.Mathematics DepartmentPasadenaUSA
  4. 4.Perimeter Institute for Theoretical PhysicsWaterlooCanada
  5. 5.Department of MathematicsUniversity of TorontoTorontoCanada

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