D-modules on rigid analytic spaces

TL;DR

This paper provides an overview of D-modules on rigid analytic spaces and explores their applications to the theory of admissible locally analytic representations of p-adic Lie groups.

Contribution

It introduces the theory of -modules on rigid analytic spaces and demonstrates their relevance to p-adic representation theory.

Findings

Development of the -module framework for rigid analytic spaces

Application of -modules to p-adic Lie group representations

Insights into the structure of locally analytic representations

Abstract

We give an overview of the theory of $\wideparen{\mathcal{D}}$-modules on rigid analytic spaces and its applications to admissible locally analytic representations of $p$-adic Lie groups.