Sur l'analogie entre le système dynamique de Deninger et le topos Weil-étale

Details Sur l'analogie entre le système dynamique de Deninger et le topos Weil-étale Sur l'analogie entre le système dynamique de Deninger et le topos Weil-étale

2010-06-02

arxiv.org/abs/1006.0527v2

Mathematics

Number Theory

33 pages. Submitted version

Scientific paper

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.

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