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Tohoku Mathematical Journal
2011
September
SECOND SERIES VOL. 63, NO. 3
Tohoku Math. J.
63 (2011), 329361

Title
SUR L'ANALOGIE ENTRE LE SYSTÈME DYNAMIQUE DE DENINGER ET LE TOPOS WEILÉTALE
Author
Baptiste Morin
(Received June 2, 2010, revised July 27, 2010) 
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 Weilétale 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 Weilétale 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 Weilétale topos. This morphism is compatible with the structure mentioned above.
2000 Mathematics Subject Classification.
Primary 14F20; Secondary 14G10, 11R42.
Key words and phrases.
Deninger's dynamical system, Weilétale cohomology, topos.


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