Holonomic $\mathscr{D}$-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.