Geodesic
Riemann-Hilbert correspondence for holonomic D-modules
D’Agnolo, Andrea1 ; Kashiwara, Masaki2 
1 Dipartimento di Matematica, Università di Padova via Trieste 63 35121 Padova Italy
2 Research Institute for Mathematical Sciences, Kyoto University 606-8502 Kyoto Japan
Publications Mathématiques de l'IHÉS, Tome 123 (2016), pp. 69-197

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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.

DOI : 10.1007/s10240-015-0076-y
Keywords: Complex Manifold, Full Subcategory, Tensor Category, Natural Morphism, Distinguished Triangle

D’Agnolo, Andrea 1 ; Kashiwara, Masaki 2

1 Dipartimento di Matematica, Università di Padova via Trieste 63 35121 Padova Italy
2 Research Institute for Mathematical Sciences, Kyoto University 606-8502 Kyoto Japan 
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     title = {Riemann-Hilbert correspondence for holonomic {D-modules}},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {69--197},
     publisher = {Springer Berlin Heidelberg},
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     year = {2016},
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D’Agnolo, Andrea; Kashiwara, Masaki. Riemann-Hilbert correspondence for holonomic D-modules. Publications Mathématiques de l'IHÉS, Tome 123 (2016), pp. 69-197. doi: 10.1007/s10240-015-0076-y

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