JournalsrmiVol. 26, No. 3pp. 825–859

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

  • Zoghman Mebkhout

    Université Paris 7 Denis Diderot, France
  • Luis Narváez Macarro

    Universidad de Sevilla, Spain
Le Théorème du symbole total d'un opérateur différentiel $p$-adique cover
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Abstract

Let X{\mathcal X}^\dagger be a smooth \dagger-scheme (in the sense of Meredith) over a complete discrete valuation ring (V,m)(V, {\mathfrak m}) of unequal characteristics (0,p)(0,p) and let DX/V{\mathcal D}^\dagger_{{\mathcal X}^\dagger/V} be the sheaf of VV-linear endomorphisms of OX{\mathcal O}_{{\mathcal X}^\dagger} whose reduction modulo ms{\mathfrak m}^s is a linear differential operator of order bounded by an affine function in ss. In this paper we prove that locally there is an OX{\mathcal O}_{{\mathcal X}^\dagger}-isomorphism between the sections of DX/V{\mathcal D}^\dagger_{{\mathcal X}^\dagger/V} 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 pp-adique. Rev. Mat. Iberoam. 26 (2010), no. 3, pp. 825–859

DOI 10.4171/RMI/618