Abstract
Abstract We introduce a sheaf of infinite order differential operators 𝒟 ⌢ {\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 𝒟 ⌢ {\overset{\frown}{\mathcal{D}}} -modules. We prove analogues of Cartan’s Theorems A and B for co-admissible 𝒟 ⌢ {\overset{\frown}{\mathcal{D}}} -modules.
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