Asymptotic behaviour of tame harmonic bundles and an application to pure twistor D-modules

Asymptotic behaviour of tame harmonic bundles and an application to pure twistor D-modules / Takuro Mochizuki.

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Bibliographic Details
Main Author: Mochizuki, Takuro, 1972- (Author)
Format: eBook
Language:English
Published: Providence, Rhode Island : American Mathematical Society, [2007]
Series:Memoirs of the American Mathematical Society ; no. 870.
Subjects:
Hodge theory.
D-modules.
Vector bundles.
Harmonic maps.
D-modules
Harmonic maps
Hodge theory
Vector bundles
Online Access:Click for online access
Table of Contents:
  • ""Contents""; ""Acknowledgement""; ""Part 4. An Application to the Theory of Pure Twistor D-modules""; ""Chapter 14. Pure Twistor D-module""; ""14.1. R-module""; ""14.2. The KMS structure of R-module""; ""14.3. R-triple""; ""14.4. Specialization of the pairing""; ""14.5. Pure Twistor D-modules and Polarization""; ""14.6. Decomposition theorem""; ""Chapter 15. Prolongation of R-module Îæ""; ""15.1. Naive prolongment Îæ and the nitrations""; ""15.2. Prolongment C""; ""15.3. Comparison of [sup(I)]T[sup((Î"[sub(0)]))](c, d) and [sup(I)]T[sup((Î"[sub(0)]))](c, d)""
  • ""15.4. Relation of the filt rations of C""""15.5. The characterization of C""; ""Chapter 16. The Filtrations of C[ð[sub(t)]]""; ""16.1. The filtration U[sup((Î"[sub(0)]))]""; ""16.2. Preliminary reductions and decompositions""; ""16.3. Primitive decomposition""; ""16.4. The associated graded modules""; ""16.5. Some decompositions for Ï?[sub(t, u)]C[ð[sub(t)]]""; ""Chapter 17. The Weight Filtration on Ï?[sub(t, u)] and the Induced R-Triple""; ""17.1. The weight filtration on [sup(I)]L""; ""17.2. The filtration F[sup((Î"[sub(0)]))] and the weight filtration""
  • 17.3. Strict specializability along Z[sub(i)] = 017.4. Strict S-decomposability along Z[sub(i)] = 0
  • Chapter 18. The Sesqui-linear Pairings
  • 18.1. The sesqui-linear pairing on C
  • 18.2. The sesqui-linear pairing on the induced flat bundles
  • 18.3. Preliminary for the calculation of the specialization
  • 18.4. The specialization of the pairings
  • Chapter 19. Polarized Pure Twistor D-module and Tame Harmonic Bundles
  • 19.1. Correspondence
  • 19.2. The tameness of the corresponding harmonic bundle
  • 19.3. The existence of the prolongment
  • 19.4. The uniqueness of the prolongment19.5. The pure imaginary case
  • 19.6. The conjectures of Kashiwara and Sabbah
  • Chapter 20. The Pure Twistor D-modules on a Smooth Curve (Appendix)
  • 20.1. Pure twistor D-module and tame harmonic bundle
  • 20.2. Twistor property for push-forward
  • Part 5. Characterization of Semisimplicity by Tame Pure Imaginary Pluri-harmonic Metric
  • Chapter 21. Preliminary
  • 21.1. Miscellaneous
  • 21.2. Elementary geometry of GL(r)/U(r)
  • 21.3. Maps associated to commuting tuple of endomorphisms
  • 21.4. Preliminary for harmonic maps and harmonic bundlesChapter 22. Tame Pure Imaginary Harmonic Bundle
  • 22.1. Definition
  • 22.2. Tame pure imaginary harmonic bundle on a punctured disc
  • 22.3. Semisimplicity
  • 22.4. The maximum principle
  • 22.5. The uniqueness of tame pure imaginary pluri-harmonic metric
  • Chapter 23. The Dirichlet Problem in the Punctured Disc Case
  • 23.1. The Dirichlet problem for a sequence of the boundary values
  • 23.2. Family version
  • Chapter 24. Control of the Energy of Twisted Maps on a Kahler Surface

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