D-modules on rigid analytic spaces I

Author: 

Ardakov, K
Wadsley, S

Publication Date: 

12 July 2017

Journal: 

Journal für die Reine und Angewandte Mathematik

Last Updated: 

2019-04-26T16:47:26.547+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.

Symplectic id: 

503528

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Submitted to ORA: 

Submitted

Publication Type: 

Journal Article