Holonomic $\mathscr{D}$-modules on rigid analytic varieties

TL;DR

This paper investigates the category of holonomic D-modules on smooth rigid analytic varieties over a non-Archimedean field, establishing finiteness of their de Rham cohomology, thus advancing the understanding of p-adic analytic D-module theory.

Contribution

It introduces the study of holonomic D-modules in the rigid analytic setting and proves the finiteness of their de Rham cohomology, a key property in p-adic analysis.

Findings

Finiteness of de Rham cohomology for holonomic D-modules.

Development of the theory of holonomic D-modules on rigid analytic varieties.

Abstract

We study the category of holonomic $\mathscr{D}_{X}$-modules for a quasi-compact, quasi-separated, smooth rigid analytic variety $X$ over the field $\mathbb{C}(\!(t)\!)$. In particular, we prove finiteness of the de Rham cohomology for such modules.