Fonctions L d'Artin et nombre de Tamagawa motiviques

TL;DR

This paper introduces motivic Artin L-functions and motivic Tamagawa numbers, establishing their properties and connections to classical concepts in number theory and algebraic geometry, particularly in the context of rational points on Fano varieties.

Contribution

It defines motivic Artin L-functions via a motivic Euler product and introduces a motivic Tamagawa number that generalizes Peyre's Tamagawa number.

Findings

Motivic Artin L-functions coincide with those of Dhillon and Minac.

Motivic Tamagawa numbers specialize to Peyre's Tamagawa numbers.

Provides a motivic framework linking L-functions and Tamagawa numbers.

Abstract

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.