Tempered solutions of $\mathcal D$-modules on complex curves and formal invariants

Abstract

Let $X$ be a complex analytic curve. In this paper we prove that the subanalytic sheaf of tempered holomorphic solutions of $\mathcal D_X$-modules induces a fully faithful functor on a subcategory of germs of formal holonomic $\mathcal D_X$-modules. Further, given a germ $\mathcal M$ of holonomic $\mathcal D_X$-module, we obtain some results linking the subanalytic sheaf of tempered solutions of $\mathcal M$ and the classical formal and analytic invariants of $\mathcal M$.