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Fonctions zêta des hauteurs des variétés toriques en caractéristique positive

Abstract : We study the analytical behaviour of the height zeta function of a compactification of an algebraic torus, defined over a global field of nonzero characteristic. The analogous problem for number fields was treated before by Batyrev/Tschinkel and Salberger. These questions lie within the general framework of Manin's conjectures. First we deal with the case of a split torus, being inspired by Salberger's method, which is based on the parametrization of the rational points given by universal torsors. Then we describe a possible extension of these techniques to a motivic setting. Finally, in order to study the case of a nonsplit torus, we draw our inspiration from Batyrev and Tschinkel's ideas, which involve harmonic analysis on the torus. We obtain the expected result, modulo the computation of an invariant of the torus, which is specific to nonzero characteristic. We were able to achieve this computation only for particular families of algebraic tori.
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https://tel.archives-ouvertes.fr/tel-00004008
Contributor : Arlette Guttin-Lombard <>
Submitted on : Wednesday, December 17, 2003 - 3:31:00 PM
Last modification on : Wednesday, November 4, 2020 - 1:59:43 PM
Long-term archiving on: : Wednesday, September 12, 2012 - 12:05:39 PM

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  • HAL Id : tel-00004008, version 1

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David Bourqui. Fonctions zêta des hauteurs des variétés toriques en caractéristique positive. Mathématiques [math]. Université Joseph-Fourier - Grenoble I, 2003. Français. ⟨tel-00004008⟩

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