Let be a smooth -scheme (in the sense of Meredith) over a complete discrete valuation ring of unequal characteristics and let be the sheaf of -linear endomorphisms of whose reduction modulo is a linear differential operator of order bounded by an affine function in . In this paper we prove that locally there is an -isomorphism between the sections of and the overconvergent total symbols, and we deduce a cohomological triviality property.
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Zoghman Mebkhout, Luis Narváez Macarro, Le Théorème du symbole total d'un opérateur différentiel -adique. Rev. Mat. Iberoam. 26 (2010), no. 3, pp. 825–859DOI 10.4171/RMI/618