Riemann-Hilbert correspondence for holonomic D-modules

D’Agnolo, Andrea; Kashiwara, Masaki

Publications Mathématiques de l'IHÉS, Tome 123 (2016), pp. 69-197.

The classical Riemann-Hilbert correspondence establishes an equivalence between the triangulated category of regular holonomic $\mathcal{D}$-modules and that of constructible sheaves.

In this paper, we prove a Riemann-Hilbert correspondence for holonomic $\mathcal{D}$-modules which are not necessarily regular. The construction of our target category is based on the theory of ind-sheaves by Kashiwara-Schapira and influenced by Tamarkin’s work. Among the main ingredients of our proof is the description of the structure of flat meromorphic connections due to Mochizuki and Kedlaya.

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