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Resume Nous developpons, pour un faisceau ´  -adique sur un trait complet de ca- racteristique p> 0, la notion de variete caracteristique. Notre approche, inspiree de l'analyse micro-locale de Kashiwara et Schapira, est un pendant faisceautique de notre theorie de ramification des corps locauxorps residuel quelconque. Nous presentons la principale propriete que devrait satisfaire la variete caracteristique (conjecture de l'isogenie), et nous la demontrons pour les faisceaux de rang un sans restriction sur le trait, ou inconditionnellement sur le faisceau si le corps residuel du trait est parfait. Abstract We develop, for an  -adicsheaf 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.

Analyse Micro-Locale $\ell$-Adique en Caractéristique $p&gt;0$ le Cas d'un Trait

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