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arXiv · 1006.0527

Sur l'analogie entre le syst\`eme dynamique de Deninger et le topos Weil-\'etale

Baptiste Morin
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Abstract

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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Baptiste Morin. 2010-06-02. Sur l'analogie entre le syst\`eme dynamique de Deninger et le topos Weil-\'etale. https://arxiv.org/abs/1006.0527

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