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

Abstract

We study the category of holonomic ${\mathcal{D}}_X$-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.

22 pages, comments welcome