D-modules on rigid analytic spaces I

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 Fréchet-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.

48 pages. Comments welcome

References in corpus (3)

• Localization of modules for a semisimple Lie algebra in prime characteristic
• Noncommutative Counterparts of the Springer Resolution
• Un théorème de Beilinson-Bernstein pour les D-modules arithmétiques

Cited by in corpus (1)

• Dagger Geometry As Banach Algebraic Geometry