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HOME > Table of Contents and Abstracts > Vol. 63, No. 3
Tohoku Mathematical Journal
2011
September
SECOND SERIES VOL. 63, NO. 3
Tohoku Math. J.
63 (2011), 329-361
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Title
SUR L'ANALOGIE ENTRE LE SYSTÈME DYNAMIQUE DE DENINGER ET LE TOPOS WEIL-ÉTALE
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 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.
2000 Mathematics Subject Classification.
Primary 14F20; Secondary 14G10, 11R42.
Key words and phrases.
Deninger's dynamical system, Weil-étale cohomology, topos.
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