# D-modules on rigid analytic spaces I

Ardakov, K

12 July 2017

## Journal:

Journal für die Reine und Angewandte Mathematik

## Last Updated:

2020-09-28T04:51:16.173+01:00

## DOI:

10.1515/crelle-2016-0016

## abstract:

We introduce a sheaf of infinite order differential operators D-cap 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 Fr\'echet-Stein algebras, and use this to define
co-admissible sheaves of D-cap-modules. We prove analogues of Cartan's Theorems
A and B for co-admissible D-cap-modules.

503528