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December 2012 On a reconstruction theorem for holonomic systems
Andrea D’Agnolo, Masaki Kashiwara
Proc. Japan Acad. Ser. A Math. Sci. 88(10): 178-183 (December 2012). DOI: 10.3792/pjaa.88.178


Let $X$ be a complex manifold. The classical Riemann-Hilbert correspondence associates to a regular holonomic system $\mathcal{M}$ the $\mathbf{C}$-constructible complex of its holomorphic solutions. Let $t$ be the affine coordinate in the complex projective line. If $\mathcal{M}$ is not necessarily regular, we associate to it the ind-$\mathbf{R}$-constructible complex $G$ of tempered holomorphic solutions to $\mathcal{M}\boxtimes\mathcal{D} e^{t}$. We conjecture that this provides a Riemann-Hilbert correspondence for holonomic systems. We discuss the functoriality of this correspondence, we prove that $\mathcal{M}$ can be reconstructed from $G$ if $\dim X=1$, and we show how the Stokes data are encoded in $G$.


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Andrea D’Agnolo. Masaki Kashiwara. "On a reconstruction theorem for holonomic systems." Proc. Japan Acad. Ser. A Math. Sci. 88 (10) 178 - 183, December 2012.


Published: December 2012
First available in Project Euclid: 6 December 2012

zbMATH: 1266.32012
MathSciNet: MR3004235
Digital Object Identifier: 10.3792/pjaa.88.178

Primary: 32C38 , 32S60 , 34M40 , 35A20

Keywords: holonomic $\mathcal{D}$-modules , ind-sheaves , Riemann-Hilbert problem , Stokes phenomenon

Rights: Copyright © 2012 The Japan Academy

Vol.88 • No. 10 • December 2012
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