Formule de torsion pour le facteur epsilon d’un caractère sur une surface

Abstract

Let \({X/\mathbb{F}_q}\) be a smooth proper surface over a finite field of characteristic p > 2, and let \({\mathcal{F}}\) be a rank one smooth l-adic sheaf (l ≠ p) on a dense open subset \({U \subset X}\). In this paper, under some assumptions on the wild ramification of \({\mathcal{F}}\), we prove a torsion formula for the epsilon factor (that is the global constant) of the functional equation of the L-function \({L(U,\mathcal{F}, t)}\). Our torsion formula is a generalization to higher dimension of the classical torsion formula for the local constants.