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.
@article{PMIHES_2016__123__69_0, 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 = {http://www.numdam.org/articles/10.1007/s10240-015-0076-y/} }
TY - JOUR AU - D’Agnolo, Andrea AU - Kashiwara, Masaki 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 - http://www.numdam.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 D’Agnolo, Andrea %A Kashiwara, Masaki %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 http://www.numdam.org/articles/10.1007/s10240-015-0076-y/ %R 10.1007/s10240-015-0076-y %G en %F PMIHES_2016__123__69_0
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. http://www.numdam.org/articles/10.1007/s10240-015-0076-y/
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