Sur l'holonomie de D-modules arithmétiques associés à des F-isocristaux surconvergents sur des courbes lisses

Christine Noot-Huyghe (1) , Fabien Trihan (2)

1 IRMA - Institut de Recherche Mathématique Avancée
2 Institut de Mathématiques [Mons]

We show that the arithmetic D-module associated to an overconvergent F-isocrystal over a smooth curve is holonomic. We first prove that unipotent F-isocrystals are holonomic D-module by using the fact that such F-isocrystals come from logarithmic F-isocrystals. We deduce the general case from the semi-stable theorem for F-isocrystals over curves of Matsuda-Trihan which relies on the p-adic monodromy theorem independently proved by André, Kedlaya and Mebkhout.

Mots clés: D-modules arithmétiques; F-isocristaux surconvergents logarithmiques; théorèmes de finitude p-adique; cohomologie p-adique

Domaines: Géométrie algébrique [math.AG]

Christine Noot-Huyghe, Fabien Trihan. Sur l'holonomie de D-modules arithmétiques associés à des F-isocristaux surconvergents sur des courbes lisses. 2007. ⟨hal-00144347v1⟩