D-modules arithmétiques surcohérents. Application aux fonctions L

Daniel Caro

Abstract

We begin by proving some properties of the local cohomology defined for arithmetic D-modules such as the commutation of it with direct images and extraordinary inverse images. Furthermore, we define the notion of overcoherent arithmetic D-modules. Next we prove the stability of the overcoherence by extraordinary inverse images and direct images. Then, we obtain a cohomological formula for L-functions associated to duals of overcoherent arithmetic complexes.

Keywords: D-modules, L-functions, local cohomological functor, holonomy, Frobenius.

AMS Subject Classification: Primary 14F30.