Riemann-Hilbert correspondence for holonomic D-modules

D’Agnolo, Andrea; Kashiwara, Masaki

doi:10.1007/s10240-015-0076-y

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

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

Résumé

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.

MR Zbl

DOI : 10.1007/s10240-015-0076-y

Mots-clés : Complex Manifold, Full Subcategory, Tensor Category, Natural Morphism, Distinguished Triangle

Affiliations des auteurs :

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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     author = {D{\textquoteright}Agnolo, Andrea and Kashiwara, Masaki},
     title = {Riemann-Hilbert correspondence for holonomic {D-modules}},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {69--197},
     publisher = {Springer Berlin Heidelberg},
     address = {Berlin/Heidelberg},
     volume = {123},
     year = {2016},
     doi = {10.1007/s10240-015-0076-y},
     mrnumber = {3502097},
     zbl = {1351.32017},
     language = {en},
     url = {https://www.numdam.org/articles/10.1007/s10240-015-0076-y/}
}

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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. https://www.numdam.org/articles/10.1007/s10240-015-0076-y/

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