La Construction d’Abbes et Saito pour les Connexions Méromorphes: Aspect Formel en Dimension 1

Abstract

In [AS09], Abbes and Saito define a measure of wild ramification of $\ell$-adique sheaves at a generic point of a complete trait of characteristic $p$, with $p\ne \ell$. Adapting their construction to differential modules of characteristic zero, we show for such a module $\mathcal{M}$ a formula which expresses that geometric invariant in terms of differential forms appearing in the Levelt–Turrittin decomposition of $\mathcal{M}$.