## Some analogies between number theory and dynamical systems on foliated spaces

### Summary

In this article we describe what a cohomology theory related to zeta and $L$-functions for algebraic schemes over the integers should look like. We then point out some striking analogies with the leafwise reduced cohomology of certain foliated dynamical systems.

### Mathematics Subject Classification

14A20, 14G10, 14F99, 37C85, 37C25, 57R30, 11G10, 11G40

### Keywords/Phrases

$L$-functions of motives, leafwise cohomology, dynamical systems, foliations, $L$-functions, zeta functions