⌢𝒟-modules on rigid analytic spaces I

Abstract

Abstract We introduce a sheaf of infinite order differential operators {\overset{\frown}{\mathcal{D}}} on smooth rigid analytic spaces that is a rigid analytic quantisation of the cotangent bundle. We show that the sections of this sheaf over sufficiently small affinoid varieties are Fréchet–Stein algebras, and use this to define co-admissible sheaves of {\overset{\frown}{\mathcal{D}}} -modules. We prove analogues of Cartan’s Theorems A and B for co-admissible {\overset{\frown}{\mathcal{D}}} -modules.