The Riemann-Hilbert Correspondence for Good Meromorphic Connections (Case of a Smooth Divisor)

This chapter is similar to Chap. 5, but we add holomorphic parameters. Moreover, we assume that no jump occurs in the exponential factors, with respect to the parameters. This is the meaning of the goodness condition in the present setting. We will have to treat the Riemann-Hilbert functor in a more invariant way, and more arguments will be needed in the proof of the main result (equivalence of categories) in order to make it global with respect to the divisor. For the sake of simplicity, we will only consider the case of germs of meromorphic connections along a smooth divisor.