Wild Harmonic Bundles and Wild Pure Twistor D-modules

Abstract

We study (i) asymptotic behaviour of wild harmonic bundles, (ii) the relation between semisimple meromorphic flat connections and wild harmonic bundles, (iii) the relation between wild harmonic bundles and polarized wild pure twistor $D$-modules. As an application, we show the hard Lefschetz theorem for algebraic semisimple holonomic $D$-modules, conjectured by M. Kashiwara.

v2: Many additional explanations and reviews are included. v3: Format is changed. Some statements are slightly refined. v4: Part I is reorganized. Some statements are refined

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