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

TL;DR

This paper develops a dimension theory for G-equivariant $$-modules on smooth rigid analytic spaces, introducing weakly holonomic modules, and studies their duality and stability under operations.

Contribution

It introduces the category of weakly holonomic G-equivariant $$-modules and analyzes their duality and stability properties in the rigid analytic setting.

Findings

Established a dimension theory for coadmissible G-equivariant $$-modules.

Defined and studied weakly holonomic G-equivariant $$-modules.

Demonstrated duality and stability properties of these modules.

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.