\wideparen{𝒟}-modules on rigid analytic spaces II: Kashiwara’s equivalence

Abstract

Let X X be a smooth rigid analytic space. We prove that the category of co-admissible \wideparen {\mathcal {D}_X}-modules supported on a closed smooth subvariety Y Y of X X is naturally equivalent to the category of co-admissible \wideparen {\mathcal {D}_Y}-modules and use this result to construct a large family of pairwise non-isomorphic simple co-admissible \wideparen {\mathcal {D}_X}-modules.