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arXiv · 1501.02215

D-modules on rigid analytic spaces I

Konstantin Ardakov·Simon Wadsley
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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.

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BibTeXRIS

Konstantin Ardakov, Simon Wadsley. 2015-01-09. D-modules on rigid analytic spaces I. https://arxiv.org/abs/1501.02215

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