Riemann-Hilbert correspondence for holonomic D-modules

By A. D'agnolo, Masaki Kashiwara. Publications mathématiques (Bures-sur-Yvette), 2013

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The classical Riemann-Hilbert correspondence establishes an equivalence between the triangulated category of regular holonomic D$\mathcal{D}$-modules and that of constructible sheaves.In this paper, we prove a Riemann-Hilbert correspondence for holonomic D$\mathcal{D}$-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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/723471e01c4803ba315876e5eacfb8107b6d317b