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

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 \(\mathcal M\).