Deninger, Christopher

Some analogies between number theory and dynamical systems on foliated spaces

Doc. Math. (Bielefeld) Extra Vol. ICM Berlin 1998, Vol. I, 163-186 (1998)


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


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