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A Microlocal Riemann–Hilbert Correspondence

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Compositio Mathematica

Abstract

We present a microlocal version of the Riemann–Hilbert correspondence for regular holonomic D-modules. We show that a regular holonomic system of microdifferential equations is associated to a perverse sheaf concentrated in degree 0. Moreover, we show that this perverse sheaf can be recovered from the local system it determines on the complementary of its singular locus. We characterize the classes of perverse sheaves and local systems associated to regular holonomic systems of microdifferential equations.

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Authors and Affiliations

  1. Departamento de Matemática, Faculdade de Ciências da Universidade de Lisboa, Lisbon, Portugal

    O. Neto

  2. CMAF, Universidade de Lisboa, Av. Gama Pinto, 2, 1649-003, Lisboa, Portugal

    O. Neto

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  1. O. Neto
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Neto, O. A Microlocal Riemann–Hilbert Correspondence. Compositio Mathematica 127, 229–241 (2001). https://doi.org/10.1023/A:1017575902563

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