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Asymptotic Behaviour of Tame Harmonic Bundles and an Application to Pure Twistor $$D$$-Modules, Part 1
Takuro Mochizuki, Kyoto University, Japan
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Memoirs of the American Mathematical Society
2007; 324 pp; softcover
Volume: 185
ISBN-10: 0-8218-3942-X
ISBN-13: 978-0-8218-3942-3
List Price: US$93 Individual Members: US$55.80
Institutional Members: US\$74.40
Order Code: MEMO/185/869

The author studies the asymptotic behaviour of tame harmonic bundles. First he proves a local freeness of the prolongment of deformed holomorphic bundle by an increasing order. Then he obtains the polarized mixed twistor structure from the data on the divisors. As one of the applications, he obtains the norm estimate of holomorphic or flat sections by weight filtrations of the monodromies.

As another application, the author establishes the correspondence of semisimple regular holonomic $$D$$-modules and polarizable pure imaginary pure twistor $$D$$-modules through tame pure imaginary harmonic bundles, which is a conjecture of C. Sabbah. Then the regular holonomic version of M. Kashiwara's conjecture follows from the results of Sabbah and the author.

• Introduction
Part 1. Preliminary
• Preliminary
• Preliminary for mixed twistor structure
• Preliminary for filtrations
• Some lemmas for generically splitted case
• Model bundles
Part 2. Prolongation of Deformed Holomorphic Bundles
• Harmonic bundles on a punctured disc
• Harmonic bundles on a product of punctured discs
• The KMS-structure of the space of the multi-valued flat sections
• The induced regular $$\lambda$$-connection on $$\Delta^n\times C^\ast$$
Part 3. Limiting Mixed Twistor theorem and Some Consequence
• The induced vector bundle over $$\mathbb{P}^1$$
• Limiting mixed twistor theorem
• Norm estimate
• Bibliography
• Index