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

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.

26 pages. minor change (v2), corrected typos (v3), minor changes and corrected misprints (v4); to appear in Münster Journal of Mathematics