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 $\mathcal{M}$.

31 pages