On the analogy between L-functions and Atiyah-Bott-Lefschetz trace formulas for foliated spaces
Leichtnam, E.

Abstract. Christopher Deninger has developed an infinite dimensional cohomological formalism which would allow to prove the expected properties of the motivic L-functions (including the Dirichlet L-functions). These cohomologies are (in general) not yet constructed. Deninger has argued that they might be constructed as leafwise cohomologies associated to ramified leafwise flat vector bundles on suitable foliated spaces. In the case of number fields we propose a set of axioms allowing to make this more precise and to motivate new theorems. We also check the coherency of these axioms and from them we derive "formally" an Atiyah-Bott-Lefschetz trace formula which would imply Artin conjecture for a Galois extension of Q.

Rend. Mat. Appl. (7) 35 (2014) 1-34; pdf