Riemann-Hilbert correspondence for holonomic D-modules

Abstract

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

114pages; v.2 minor changes, 114 pp

References in corpus (2)

• On the Laplace transform for tempered holomorphic functions
• On a reconstruction theorem for holonomic systems

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• A remark on Continuous K-theory and Fourier-Sato transform