Le théorème du symbole total d'un opérateur différentiel $p$-adique d'échelon $h\geq0$

Abstract

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.