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- W64657759 abstract "This chapter is similar to Chap. 10, but we now assume that D is a divisor with normal crossings. We start by proving the many-variable version of the Hukuhara–Turrittin theorem, that we have already encountered in the case of a smooth divisor. It will be instrumental for making the link between formal and holomorphic aspects of the theory. The new point in the proof of the Riemann–Hilbert correspondence is the presence of non-Hausdorff éalé spaces, and we need to use the level structure to prove the local essential surjectivity of the Riemann–Hilbert functor. As an application of the Riemann–Hilbert correspondence in the good case and of the fundamental results of K. Kedlaya and T. Mochizuki on the elimination of turning points by complex blowing-ups, we prove a conjecture of M. Kashiwara asserting that the Hermitian dual of a holonomic $$mathcal{D}$$ -module is holonomic, generalizing the original result of M. Kashiwara for regular holonomic $$mathcal{D}$$ -modules to possibly irregular holonomic $$mathcal{D}$$ -modules and the result of Chap. 6 to higher dimensions." @default.
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- W64657759 date "2012-07-25" @default.
- W64657759 modified "2023-09-25" @default.
- W64657759 title "Good Meromorphic Connections (Analytic Theory) and the Riemann–Hilbert Correspondence" @default.
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- W64657759 doi "https://doi.org/10.1007/978-3-642-31695-1_12" @default.
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