Analyse micro-locale l-adique en caracteristique p>0: Le cas d'un trait

Ahmed Abbes (1) , Takeshi Saito (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 Department of Mathematical Sciences

We develop, for an l-adic etale 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.

Mots clés: algebraic geometry; number theory

Domaines: Géométrie algébrique [math.AG]; Théorie des nombres [math.NT]

Ahmed Abbes, Takeshi Saito. Analyse micro-locale l-adique en caracteristique p>0: Le cas d'un trait. Research Institute for Mathematical Sciences, 2009, 45, pp.25-74. ⟨hal-00374047⟩