Title: Some Analogies Between Number Theory and Dynamical Systems on Foliated Spaces

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.

1991 Mathematics Subject Classification: Primary 14A20; Secondary 14G10, 14F99, 58F18, 58F20.

Keywords and Phrases: $L$-functions of motives, leafwise cohomology, dynamical systems, foliations.

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