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

We study the category of holonomic ${\mathcal{D}}_X$-modules for a quasi-compact, quasi-separated, smooth rigid analytic variety $X$ over the field $\mathbb{C}(\text{\hspace{0.17em}⁣}(t)\text{\hspace{0.17em}⁣})$. In particular, we prove finiteness of the de Rham cohomology for such modules.