On the analogy between Arithmetic Geometry and foliated spaces

Abstract

Christopher Deninger has developed an infinite dimensional cohomological formalism which allows to prove the expected properties of the arithmetical Zeta functions (including the Riemann Zeta function). These cohomologies are (in general) not yet constructed. Deninger has argued that these cohomologies might be constructed as leafwise cohomologies of suitable foliated spaces. We shall review some recent results which support this hope.

Keywords

• foliations
• dynamical
• lefschetz
• trace