Stokes structure of wild difference modules

Abstract

We formulate and prove a Riemann--Hilbert correspondence between two categories: wild difference modules and wild Stokes-filtered $\mathscr{A}_{\rm{per}}$-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.