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September, 2010 Le Théorème du symbole total d'un opérateur différentiel $p$-adique
Zoghman Mebkhout , Luis Narváez Macarro
Rev. Mat. Iberoamericana 26(3): 825-859 (September, 2010).


Let ${\mathcal X}^\dagger$ be a smooth $\dagger$-scheme (in the sense of Meredith) over a complete discrete valuation ring $(V, {\mathfrak m})$ of unequal characteristics $(0,p)$ and let ${\mathcal D}^\dagger_{{\mathcal X}^\dagger/V}$ be the sheaf of $V$-linear endomorphisms of ${\mathcal O}_{{\mathcal X}^\dagger}$ whose reduction modulo ${\mathfrak m}^s$ is a linear differential operator of order bounded by an affine function in $s$. In this paper we prove that locally there is an ${\mathcal O}_{{\mathcal X}^\dagger}$-isomorphism between the sections of ${\mathcal D}^\dagger_{{\mathcal X}^\dagger/V}$ 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 $p$-adique." Rev. Mat. Iberoamericana 26 (3) 825 - 859, September, 2010.


Published: September, 2010
First available in Project Euclid: 27 August 2010

zbMATH: 1213.14042

Primary: 14F10 , 14F30

Keywords: $\dagger$-adic differential operator , $\dagger$-scheme , affinoid algebra , Dwork-Monsky-Washnitzer algebra

Rights: Copyright © 2010 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.26 • No. 3 • September, 2010
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