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arXiv · 1208.6104

On a reconstruction theorem for holonomic systems

Andrea D'Agnolo·Masaki Kashiwara
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Abstract

Let X be a complex manifold. The classical Riemann-Hilbert correspondence associates to a regular holonomic system M the C-constructible complex of its holomorphic solutions. Denote by t the affine coordinate in the complex projective line. If M is not necessarily regular, we associate to it the ind-R-constructible complex G of tempered holomorphic solutions to the exterior product of M with the D-module associated with the exponential e^t. We conjecture that this provides a Riemann-Hilbert correspondence for holonomic systems. We discuss the functoriality of this correspondence, we prove that M can be reconstructed from G if X has dimension 1, and we show how the Stokes data are encoded in G.

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Andrea D'Agnolo, Masaki Kashiwara. 2012-09-03. On a reconstruction theorem for holonomic systems. https://doi.org/10.3792/pjaa.88.178

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