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

Abstract

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