Le Théorème du symbole total d'un opérateur différentiel p-adique

摘要

Let Χ~? be a smooth ?-scheme (in the sense of Meredith) over a complete discrete valuation ring (V,m) of unequal characteristics (0,p) and let D~?_(Χ?/V) be the sheaf of V-linear endomorphisms of OΧ~? whose reduction modulo m~s is a linear differential operator of order bounded by an affine function in s. In this paper we prove that locally there is an OΧ~? -isomorphism between the sections of D ~?_(Χ?/V) and the overconvergent total symbols, and we deduce a cohomological triviality property.