Stokes-Perverse Sheaves on Riemann Surfaces

In this chapter, we introduce the global notion of Stokes-perverse sheaves on a Riemann surface. The Riemann-Hilbert correspondence of the next chapter will be an equivalence between holonomic D-modules on the Riemann surface and Stokes-perverse sheaves on it. If k is a subfield of C, this allows one to speak of a k-structure on a holonomic D-module when the corresponding Stokes-perverse is defined over k.