On a relation between Deninger's foliated dynamical systems and Connes-Consani's adelic spaces

TL;DR

This paper explores the connection between Deninger's foliated dynamical systems and Connes-Consani's adelic spaces, providing a geometric perspective on class field theory within the framework of arithmetic topology.

Contribution

It establishes a novel relation between dynamical systems and adelic spaces, illuminating geometric insights into class field theory and the analogy between knots and primes.

Findings

Identifies a link between Deninger's dynamical systems and adelic spaces.

Provides a geometric interpretation of class field theory.

Enhances the analogy between knots and primes in arithmetic topology.

Abstract

We give a relation between Deninger's foliated dynamical systems associated to abelian number fields and Connes-Consani's adelic spaces. It fits with the analogy between knots and primes in arithmetic topology and lights up a geometric view of class field theory.