Stokes structure of wild difference modules

We formulate and prove a Riemann–Hilbert correspondence between two categories: wild difference modules and wild Stokes-filtered ${\mathcal{A}}_{\mathrm{p}\mathrm{e}\mathrm{r}}$-modules. This correspondence is motivated by the Riemann–Hilbert correspondence for germs of meromorphic connections in one variable due to Deligne–Malgrange. It also generalizes the Riemann–Hilbert correspondence for mild difference modules.