Sur l'holonomie de D-modules arithm\'etiques associ\'es \`a des F-isocristaux surconvergents sur des courbes lisses

Abstract

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 Andr\'e, Kedlaya and Mebkhout. The main result has already been proved by D. Caro.