Tohoku Mathematical Journal

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

Baptiste Morin

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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-étale 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-étale topos. This analogy extends to arithmetic schemes. Over a prime number $p$ and over the archimedean place of $\boldsymbol{Q}$, we define a morphism from a topos associated to Deninger's dynamical system to the Weil-étale topos. This morphism is compatible with the structure mentioned above.

Article information

Tohoku Math. J. (2), Volume 63, Number 3 (2011), 329-361.

First available in Project Euclid: 11 October 2011

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Zentralblatt MATH identifier

Primary: 14F20: Étale and other Grothendieck topologies and (co)homologies
Secondary: 14G10: Zeta-functions and related questions [See also 11G40] (Birch- Swinnerton-Dyer conjecture) 11R42: Zeta functions and $L$-functions of number fields [See also 11M41, 19F27]

Deninger's dynamical system Weil-étale cohomology topos


Morin, Baptiste. Sur l'analogie entre le système dynamique de Deninger et le topos Weil-étale. Tohoku Math. J. (2) 63 (2011), no. 3, 329--361. doi:10.2748/tmj/1318338946.

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