Fourier-Laplace transform of irreducible regular differential systems on the Riemann sphere

Abstract

We show that the Fourier-Laplace transform of an irreducible regular differential system on the Riemann sphere underlies, when one only considers the part at finite distance, a polarizable regular twistor $\mathcal{D}$-module. The associated holomorphic bundle out of the origin is therefore equipped with a natural harmonic metric with a tame behaviour near the origin.

13+11 pages, AMSlatex. Original version followed by an Erratum added may 2007 after publication

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