%0 Journal Article
%T Sur l'analogie entre le syst¨¨me dynamique de Deninger et le topos Weil-¨¦tale
%A Baptiste Morin
%J Mathematics
%D 2010
%I arXiv
%X We express some basic properties of Deninger's conjectural dynamical system in terms of morphisms of topoi. Then we show that the current definition of the Weil-\'etale topos satisfies these properties. In particular, the flow, the closed orbits, the fixed points of the flow and the foliation in characteristic $p$ are well defined on the Weil-\'etale topos. This analogy extends to arithmetic schemes. Over a prime number $p$ and over the archimedean place of $\mathbb{Q}$, we define a morphism from a topos associated to Deninger's dynamical system to the Weil-\'etale topos. This morphism is compatible with the structure mentioned above.
%U http://arxiv.org/abs/1006.0527v2