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

  • Zoghman Mebkhout

    Université Paris 7 Denis Diderot, France
  • Luis Narváez Macarro

    Universidad de Sevilla, Spain

Abstract

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.

Cite this article

Zoghman Mebkhout, Luis Narváez Macarro, Le Théorème du symbole total d'un opérateur différentiel -adique. Rev. Mat. Iberoam. 26 (2010), no. 3, pp. 825–859

DOI 10.4171/RMI/618