Revista Matemática Iberoamericana


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Volume 27, Issue 1, 2011, pp. 39–92
DOI: 10.4171/RMI/630

Published online: 2011-04-30

Le théorème du symbole total d’un opérateur différentiel p-adique d’échelon h ≥ 0

Zoghman Mebkhout[1]

(1) Université Paris 7 Denis Diderot, Paris, France

In this article we prove the total symbol theorem for the $p$-adic differential operators of degree $h\geq 0$ for the echelon filtration and the noetherianity of the ring of the $p$-adic differential operators of degree $h\geq 0$ for the echelon filtration over a $\dagger$-adic affine smooth scheme small enough.

Keywords: p-adic differential operator, p-adic differential operator of h ≥ 0 echelon, total symbol, division, continuity, noetherianity, p-adic de Rham cohomology.

Mebkhout Zoghman: Le théorème du symbole total d’un opérateur différentiel p-adique d’échelon h ≥ 0. Rev. Mat. Iberoamericana 27 (2011), 39-92. doi: 10.4171/RMI/630