Weakly holonomic equivariant $\mathcal{D}$-modules on rigid analytic spaces

Abstract

Let G be a $p$-adic Lie group. We develop a dimension theory for coadmissible G-equivariant $\mathcal{D}$-modules on smooth rigid analytic spaces. We introduce the category of weakly holonomic G-equivariant $\mathcal{D}$-modules, study its duality and its preservation under various operations.