Nearby Cycles of Stokes-Filtered Local Systems

Abstract

In this chapter, we define a nearby cycle functor for a good Stokes-filtered local system on (X, D), relative to a holomorphic function whose zero set is contained in the normal crossing divisor D. We then show that the Riemann–Hilbert correspondence of Chap. 12 is compatible with taking nearby cycles, either in the sense of irregular nearby cycles for meromorphic flat bundles as defined in Chap. 14, or as defined for Stokes-filtered local systems in this chapter.