04073nam 2200565 450 991081243770332120180613001308.01-4704-0473-7(CKB)3360000000465053(EBL)3114135(MiAaPQ)EBC3114135(RPAM)14559896(PPN)195417585(EXLCZ)99336000000046505320150410h20072007 uy| 0engur|n|---|||||rdacontentrdamediardacarrierAsymptotic behaviour of tame harmonic bundles and an application to pure twistor D-modulesPart 1 /Takuro MochizukiProvidence, Rhode Island :American Mathematical Society,[2007]©20071 online resource (344 p.)Memoirs of the American Mathematical Society,0065-9266 ;number 869Description based upon print version of record.0-8218-3942-X Includes bibliographical references and index.""Contents""; ""Acknowledgement""; ""Chapter 1. Introduction""; ""1.1. Simpson's Meta-Theorem""; ""1.2. The purposes in this paper""; ""1.3. On the purpose (1)""; ""1.4. On the purpose (2)""; ""1.5. Some Remark""; ""1.6. The outline of the paper""; ""Part 1. Preliminary""; ""Chapter 2. Preliminary""; ""2.1. Notation""; ""2.2. Prolongation by an increasing order""; ""2.3. Preliminary for Î?c-equivariant bundle""; ""2.4. Some elementary preliminary for convexity""; ""2.5. Some lemmas for functions on a disc""; ""2.6. An elementary remark on some distributions""""2.7. Preliminary from elementary linear algebra""""2.8. Preliminary from complex differential geometry""; ""2.9. Preliminary from functional analysis""; ""2.10. An estimate of the norms of Higgs field and the conjugate""; ""2.11. Convergency of the sequence of harmonic bundles""; ""2.12. Higgs field and twisted map""; ""Chapter 3. Preliminary for Mixed Twistor Structure""; ""3.1. P[sup(1)]-holomorphic vector bundle over X x P[sup(1)]""; ""3.2. Equivariant P[sup(1)]-holomorphic bundle over X x P[sup(1)]""; ""3.3. Tate objects and O(p,q)""; ""3.4. Equivalence of some categories""""3.5. Variation of P[sup(1)]-holomorphic bundles""""3.6. The twistor nilpotent orbit""; ""3.7. Split polarized mixed twistor structure and the nilpotent orbit""; ""3.8. The induced tuple on the divisor""; ""3.9. Translation of some results due to Kashiwara, Kawai and Saito""; ""3.10. R-triple in dimension 0 and twistor structure""; ""Chapter 4. Preliminary for Filtrations""; ""4.1. Filtrations and decompositions on a vector space""; ""4.2. Filtrations and decompositions on a vector bundle""; ""4.3. Compatibility of the filtrations and nilpotent maps""; ""4.4. Extension of splittings""""4.5. Compatibility of the filtrations and nilpotent maps on the divisors""""Chapter 5. Some Lemmas for Generically Splitted Case""; ""5.1. Filtrations""; ""5.2. Compatibility of morphisms and filtrations""; ""Chapter 6. Model Bundles""; ""6.1. Basic example I""; ""6.2. Basic example II""; ""Part 2. Prolongation of Deformed Holomorphic Bundles""; ""Chapter 7. Harmonic Bundles on a Punctured Disc""; ""7.1. Simpson's main estimate""; ""7.2. The KMS-structure of tame harmonic bundles on a punctured disc""; ""7.3. Basic comparison due to Simpson""; ""7.4. Multi-valued flat sections""Memoirs of the American Mathematical Society ;no. 869.Hodge theoryD-modulesVector bundlesHarmonic mapsHodge theory.D-modules.Vector bundles.Harmonic maps.514.74Mochizuki Takuro1972-319920MiAaPQMiAaPQMiAaPQBOOK9910812437703321Asymptotic behaviour of tame harmonic bundles and an application to pure twistor D-modules3971684UNINA