Stokes Matrices and Meromorphic Classification

Abstract

We will denote the differential fields C({z}) and C((z)) by K and $\hat{K}$. The classification of differential modules over $\hat{K}$, given in Sect. 3.2, associates with a differential module M a triple Trip(M)=(V, {V _q }, γ). More precisely, a tannakian category Gr₁ was defined, which has as objects the above triples. The functor Trip: ${\text{Dif}}{{\text{f}}_{{\hat{K}}}} \to {\text{G}}{{\text{r}}_1}$ from the category of the differential modules over $\hat{K}$ to the category of triples was shown to be an equivalence of tannakian categories.