The classical Riemann-Hilbert correspondence establishes an equivalence between the triangulated category of regular holonomic -modules and that of constructible sheaves.
In this paper, we prove a Riemann-Hilbert correspondence for holonomic -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.
Accepted:
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DOI: 10.1007/s10240-015-0076-y
Andrea D’Agnolo 1; Masaki Kashiwara 2
@article{PMIHES_2016__123__69_0,
author = {Andrea D{\textquoteright}Agnolo and Masaki Kashiwara},
title = {Riemann-Hilbert correspondence for holonomic {D-modules}},
journal = {Publications Math\'ematiques de l'IH\'ES},
pages = {69--197},
year = {2016},
publisher = {Springer Berlin Heidelberg},
address = {Berlin/Heidelberg},
volume = {123},
doi = {10.1007/s10240-015-0076-y},
mrnumber = {3502097},
zbl = {1351.32017},
language = {en},
url = {https://pmihes.centre-mersenne.org/articles/10.1007/s10240-015-0076-y/}
}
TY - JOUR AU - Andrea D’Agnolo AU - Masaki Kashiwara TI - Riemann-Hilbert correspondence for holonomic D-modules JO - Publications Mathématiques de l'IHÉS PY - 2016 SP - 69 EP - 197 VL - 123 PB - Springer Berlin Heidelberg PP - Berlin/Heidelberg UR - https://pmihes.centre-mersenne.org/articles/10.1007/s10240-015-0076-y/ DO - 10.1007/s10240-015-0076-y LA - en ID - PMIHES_2016__123__69_0 ER -
%0 Journal Article %A Andrea D’Agnolo %A Masaki Kashiwara %T Riemann-Hilbert correspondence for holonomic D-modules %J Publications Mathématiques de l'IHÉS %D 2016 %P 69-197 %V 123 %I Springer Berlin Heidelberg %C Berlin/Heidelberg %U https://pmihes.centre-mersenne.org/articles/10.1007/s10240-015-0076-y/ %R 10.1007/s10240-015-0076-y %G en %F PMIHES_2016__123__69_0
Andrea D’Agnolo; Masaki Kashiwara. Riemann-Hilbert correspondence for holonomic D-modules. Publications Mathématiques de l'IHÉS, Volume 123 (2016), pp. 69-197. doi: 10.1007/s10240-015-0076-y
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