2010/06/02 by Baptiste Morin, Morin, Baptiste
Mathematics · #Algebraic Geometry (math.AG) #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.DS #math.NT
paper · pdf · doi:10.48550/arxiv.1006.0527
33 pages. Submitted version
arxiv created 2010/10/17 · arxiv updated 2010/10/19
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 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.