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Let $X$ be a complex analytic curve. In this paper we prove that thesubanalytic sheaf of tempered holomorphic solutions of $\mathcal D_X$-modulesinduces 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 oftempered solutions of $\mathcal M$ and the classical formal and analyticinvariants of $\mathcal M$.

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