D-modules on rigid analytic spaces II: Kashiwara's equivalence

TL;DR

This paper extends the theory of D-modules to rigid analytic spaces, proving an equivalence of categories for modules supported on subvarieties and constructing many simple modules, advancing the understanding of their structure.

Contribution

It establishes Kashiwara's equivalence for coadmissible D-modules on rigid analytic spaces and constructs numerous non-isomorphic simple modules.

Findings

Proved category equivalence for coadmissible D-modules supported on subvarieties.

Constructed a large family of non-isomorphic simple coadmissible D-modules.

Enhanced the structural understanding of D-modules in rigid analytic geometry.

Abstract

We prove that the category of coadmissible D-cap-modules on a smooth rigid analytic space supported on a closed smooth subvariety is naturally equivalent to the category of coadmissible D-cap-modules on the subvariety, and use this result to construct a large family of pairwise non-isomorphic simple coadmissible D-cap-modules.