Analyse Micro-Locale $\ell$-Adique en Caractéristique $p>0$ le Cas d’un Trait

Abstract

We develop, for an $\ell$-adic étale sheaf on a complete trait of characteristic $p>0$, the notion of characteristic variety. Our approach, inspired by the microlocal analysis of Kashiwara and Schapira, is a complement to our ramification theory for local fields with general residue fields. We formulate the main property that should be satisfied by the characteristic variety (the isogeny conjecture), and prove it for rank one sheaves unconditionally on the trait, or unconditionally on the sheaf if the residue field of the trait is perfect.