Reconstructing global fields from dynamics in the abelianized Galois group

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.

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