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A Microlocal Riemann–Hilbert Correspondence

Published online by Cambridge University Press:  04 December 2007

O. Neto
O. Neto
Affiliation:
Departamento de Matemática, Faculdade de Ciências da Universidade de Lisboa, Lisbon, Portugal. E-mail: [email protected] and CMAF, Universidade de Lisboa, Av. Gama Pinto, 2, 1649-003 Lisboa, Portugal
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Abstract

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We present a microlocal version of the Riemann–Hilbert correspondence for regular holonomic $\cal D$-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.

Keywords

holonomic systemsperverse sheavesRiemann–Hilbert correspondencemicrolocal analysis
Type
Research Article
Information
Compositio Mathematica , Volume 127 , Issue 3 , July 2001 , pp. 229 - 241
Copyright
© 2001 Kluwer Academic Publishers