Reconstructing global fields from dynamics in the abelianized Galois group
Number Theory
2017-06-15 v1 Dynamical Systems
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.
Cite
@article{arxiv.1706.04517,
title = {Reconstructing global fields from dynamics in the abelianized Galois group},
author = {Gunther Cornelissen and Xin Li and Matilde Marcolli and Harry Smit},
journal= {arXiv preprint arXiv:1706.04517},
year = {2017}
}
Comments
16 pages; replaces the part of arXiv:1009.0736 dealing with dynamical systems; results related to L-series have been moved to a separate preprint by the authors and Bart de Smit, of which the preliminary section (fixing notations) overlaps with that of the current paper