Wild Harmonic Bundles and Wild Pure Twistor D-modules

TL;DR

This paper investigates the asymptotic properties of wild harmonic bundles, their connections to meromorphic flat connections and wild pure twistor D-modules, and proves the hard Lefschetz theorem for certain algebraic D-modules.

Contribution

It establishes new links between wild harmonic bundles, meromorphic flat connections, and wild pure twistor D-modules, and proves a conjecture by Kashiwara.

Findings

Proved the hard Lefschetz theorem for algebraic semisimple holonomic D-modules.

Clarified the relationship between wild harmonic bundles and wild pure twistor D-modules.

Analyzed the asymptotic behavior of wild harmonic bundles.

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.