- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:45
Revista Matemática Iberoamericana
Rev. Mat. Iberoamericana
RMI
0213-2230
2235-0616
General
10.4171/RMI
http://www.ems-ph.org/doi/10.4171/RMI
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2012)
26
2010
3
Le Théorème du symbole total d'un opérateur différentiel $p$-adique
Zoghman
Mebkhout
Université Paris 7 Denis Diderot, PARIS CEDEX 05, FRANCE
Luis
Narváez Macarro
Universidad de Sevilla, SEVILLA, SPAIN
Affinoid algebra, Dwork-Monsky-Washnitzer algebra, †-scheme, †-adic differential operator
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.
Algebraic geometry
General
825
859
10.4171/RMI/618
http://www.ems-ph.org/doi/10.4171/RMI/618