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

Giovanni Morando — 2009

Annales de l’institut Fourier

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

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