Fonctions L d'Artin et nombre de Tamagawa motiviques

David Bourqui (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

In the first part of this text, we define motivic Artin L-fonctions via a motivic Euler product, and show that they coincide with the analogous functions introduced by Dhillon and Minac. In the second part, we define under some assumptions a motivic Tamagawa number and show that it specializes to the Tamagawa number introduced by Peyre in the context of Manin's conjectures about rational points of bounded height on Fano varieties.

Mots clés: Motivic Artin L-function; Tamagawa number; motivic Tamagawa number; motivic Euler product; height zeta function

Domaines: Géométrie algébrique [math.AG]; Théorie des nombres [math.NT]

David Bourqui. Fonctions L d'Artin et nombre de Tamagawa motiviques. New York Journal of Mathematics, 2010, 16, pp.179-233. ⟨hal-00315608⟩