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Asymptotic behaviour of tame harmonic bundles and an application to pure twistor D-modules . Part 1 / / Takuro Mochizuki
Asymptotic behaviour of tame harmonic bundles and an application to pure twistor D-modules . Part 1 / / Takuro Mochizuki
Autore Mochizuki Takuro <1972->
Pubbl/distr/stampa Providence, Rhode Island : , : American Mathematical Society, , [2007]
Descrizione fisica 1 online resource (344 p.)
Disciplina 514.74
Collana Memoirs of the American Mathematical Society
Soggetto topico Hodge theory
D-modules
Vector bundles
Harmonic maps
Soggetto genere / forma Electronic books.
ISBN 1-4704-0473-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto ""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""
Record Nr. UNINA-9910480401303321
Mochizuki Takuro <1972->  
Providence, Rhode Island : , : American Mathematical Society, , [2007]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Asymptotic behaviour of tame harmonic bundles and an application to pure twistor D-modules / / Takuro Mochizuki
Asymptotic behaviour of tame harmonic bundles and an application to pure twistor D-modules / / Takuro Mochizuki
Autore Mochizuki Takuro <1972->
Pubbl/distr/stampa Providence, Rhode Island : , : American Mathematical Society, , [2007]
Descrizione fisica 1 online resource (262 p.)
Disciplina 514.74
Collana Memoirs of the American Mathematical Society
Soggetto topico Hodge theory
D-modules
Vector bundles
Harmonic maps
Soggetto genere / forma Electronic books.
ISBN 1-4704-0474-5
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto ""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((λ[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((λ[sub(0)]))] and the weight filtration""
""17.3. Strict specializability along Z[sub(i)] = 0""""17.4. 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 prolongment""""19.5. 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 bundles""""Chapter 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""
""24.1. Around smooth points of divisors""
Record Nr. UNINA-9910480643203321
Mochizuki Takuro <1972->  
Providence, Rhode Island : , : American Mathematical Society, , [2007]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Asymptotic behaviour of tame harmonic bundles and an application to pure twistor D-modules / / Takuro Mochizuki
Asymptotic behaviour of tame harmonic bundles and an application to pure twistor D-modules / / Takuro Mochizuki
Autore Mochizuki Takuro <1972->
Pubbl/distr/stampa Providence, Rhode Island : , : American Mathematical Society, , [2007]
Descrizione fisica 1 online resource (262 p.)
Disciplina 514.74
Collana Memoirs of the American Mathematical Society
Soggetto topico Hodge theory
D-modules
Vector bundles
Harmonic maps
ISBN 1-4704-0474-5
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto ""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((λ[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((λ[sub(0)]))] and the weight filtration""
""17.3. Strict specializability along Z[sub(i)] = 0""""17.4. 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 prolongment""""19.5. 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 bundles""""Chapter 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""
""24.1. Around smooth points of divisors""
Record Nr. UNINA-9910788743303321
Mochizuki Takuro <1972->  
Providence, Rhode Island : , : American Mathematical Society, , [2007]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Asymptotic behaviour of tame harmonic bundles and an application to pure twistor D-modules . Part 1 / / Takuro Mochizuki
Asymptotic behaviour of tame harmonic bundles and an application to pure twistor D-modules . Part 1 / / Takuro Mochizuki
Autore Mochizuki Takuro <1972->
Pubbl/distr/stampa Providence, Rhode Island : , : American Mathematical Society, , [2007]
Descrizione fisica 1 online resource (344 p.)
Disciplina 514.74
Collana Memoirs of the American Mathematical Society
Soggetto topico Hodge theory
D-modules
Vector bundles
Harmonic maps
ISBN 1-4704-0473-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto ""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""
Record Nr. UNINA-9910788743603321
Mochizuki Takuro <1972->  
Providence, Rhode Island : , : American Mathematical Society, , [2007]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Asymptotic behaviour of tame harmonic bundles and an application to pure twistor D-modules / / Takuro Mochizuki
Asymptotic behaviour of tame harmonic bundles and an application to pure twistor D-modules / / Takuro Mochizuki
Autore Mochizuki Takuro <1972->
Pubbl/distr/stampa Providence, Rhode Island : , : American Mathematical Society, , [2007]
Descrizione fisica 1 online resource (262 p.)
Disciplina 514.74
Collana Memoirs of the American Mathematical Society
Soggetto topico Hodge theory
D-modules
Vector bundles
Harmonic maps
ISBN 1-4704-0474-5
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto ""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((λ[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((λ[sub(0)]))] and the weight filtration""
""17.3. Strict specializability along Z[sub(i)] = 0""""17.4. 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 prolongment""""19.5. 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 bundles""""Chapter 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""
""24.1. Around smooth points of divisors""
Record Nr. UNINA-9910819099103321
Mochizuki Takuro <1972->  
Providence, Rhode Island : , : American Mathematical Society, , [2007]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Asymptotic behaviour of tame harmonic bundles and an application to pure twistor D-modules . Part 1 / / Takuro Mochizuki
Asymptotic behaviour of tame harmonic bundles and an application to pure twistor D-modules . Part 1 / / Takuro Mochizuki
Autore Mochizuki Takuro <1972->
Pubbl/distr/stampa Providence, Rhode Island : , : American Mathematical Society, , [2007]
Descrizione fisica 1 online resource (344 p.)
Disciplina 514.74
Collana Memoirs of the American Mathematical Society
Soggetto topico Hodge theory
D-modules
Vector bundles
Harmonic maps
ISBN 1-4704-0473-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto ""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""
Record Nr. UNINA-9910812437703321
Mochizuki Takuro <1972->  
Providence, Rhode Island : , : American Mathematical Society, , [2007]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Donaldson type invariants for algebraic surfaces : transition of moduli stacks / / Takuro Mochizuki
Donaldson type invariants for algebraic surfaces : transition of moduli stacks / / Takuro Mochizuki
Autore Mochizuki Takuro <1972->
Edizione [1st ed. 2009.]
Pubbl/distr/stampa Berlin, : Springer, c2009
Descrizione fisica 1 online resource (XXIII, 383 p.)
Disciplina 516.35
Collana Lecture notes in mathematics
Soggetto topico Surfaces, Algebraic
Invariants
Moduli theory
ISBN 9783540939139
354093913X
Classificazione 14D2014J6014J80
MAT 142f
MAT 146f
SI 850
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Preliminaries -- Parabolic L-Bradlow Pairs -- Geometric Invariant Theory and Enhanced Master Space -- Obstruction Theories of Moduli Stacks and Master Spaces -- Virtual Fundamental Classes -- Invariants.
Record Nr. UNINA-9910484256703321
Mochizuki Takuro <1972->  
Berlin, : Springer, c2009
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Mixed Twistor D-modules / / by Takuro Mochizuki
Mixed Twistor D-modules / / by Takuro Mochizuki
Autore Mochizuki Takuro <1972->
Edizione [1st ed. 2015.]
Pubbl/distr/stampa Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015
Descrizione fisica 1 online resource (XX, 487 p.)
Disciplina 515.353
Collana Lecture Notes in Mathematics
Soggetto topico Functions of complex variables
Geometry, Algebraic
Several Complex Variables and Analytic Spaces
Algebraic Geometry
ISBN 3-319-10088-2
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Introduction -- Preliminary -- Canonical prolongations -- Gluing and specialization of r-triples -- Gluing of good-KMS r-triples -- Preliminary for relative monodromy filtrations -- Mixed twistor D-modules -- Infinitesimal mixed twistor modules -- Admissible mixed twistor structure and variants -- Good mixed twistor D-modules -- Some basic property -- Dual and real structure of mixed twistor D-modules -- Derived category of algebraic mixed twistor D-modules -- Good systems of ramified irregular values.
Record Nr. UNINA-9910131641303321
Mochizuki Takuro <1972->  
Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Periodic monopoles and difference modules / / Takuro Mochizuki
Periodic monopoles and difference modules / / Takuro Mochizuki
Autore Mochizuki Takuro <1972->
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2022]
Descrizione fisica 1 online resource (336 pages)
Disciplina 516.36
Collana Lecture Notes in Mathematics
Soggetto topico Geometry, Differential
Geometria diferencial
Soggetto genere / forma Llibres electrònics
ISBN 9783030945008
9783030944995
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Preface -- Acknowledgements -- Contents -- 1 Introduction -- 1.1 Background and Motivation -- 1.2 Monopoles of GCK-Type -- 1.3 Previous Works on Monopoles and Algebraic Objects -- 1.3.1 SU(2)-Monopoles with Finite Energy on R3 -- 1.3.2 The Correspondence due to Charbonneau and Hurtubise -- 1.3.3 Remark -- 1.4 Review of the Kobayashi-Hitchin Correspondences for λ-Flat Bundles -- 1.4.1 Harmonic Bundles and Their Underlying λ-Flat Bundles -- 1.4.2 Kobayashi-Hitchin Correspondences in the Smooth Case -- 1.4.3 Tame Harmonic Bundles and Regular Filtered λ-Flat Bundles -- 1.4.4 Wild Harmonic Bundles and Good Filtered λ-Flat Bundles -- 1.5 Equivariant Instantons and the Underlying Holomorphic Objects -- 1.5.1 Instantons and the Underlying Holomorphic Bundles -- 1.5.2 Instantons and Harmonic Bundles -- 1.5.3 Instantons and Monopoles -- 1.5.4 Instantons and Monopoles as Harmonic Bundles of Infinite Rank -- 1.5.4.1 Instantons as Harmonic Bundles of Infinite Rank -- 1.5.4.2 The Underlying λ-Flat Bundles of Infinite Rank -- 1.5.4.3 Monopoles as Harmonic Bundles of Infinite Rank -- 1.6 Difference Modules with Parabolic Structure -- 1.6.1 Difference Modules -- 1.6.2 Parabolic Structure of Difference Modules at Finite Place -- 1.6.3 Good Parabolic Structure at ∞ -- 1.6.4 Parabolic Difference Modules -- 1.6.5 Degree and Stability Condition -- 1.6.6 Easy Examples of Stable Parabolic Difference Modules (1) -- 1.6.6.1 The Case Where (∞) Is Even -- 1.6.6.2 The Case Where (∞) Is Odd -- 1.6.7 Easy Examples of Stable Parabolic Difference Modules (2) -- 1.7 Kobayashi-Hitchin Correspondences for Periodic Monopoles -- 1.7.1 The Correspondence in the Case λ=0 -- 1.7.1.1 Mini-complex Structure -- 1.7.1.2 Mini-holomorphic Bundles Associated with Monopoles -- 1.7.1.3 Dirac Type Singularity -- 1.7.1.4 Meromorphic Extension and Filtered Extension at Infinity.
1.7.1.5 Kobayashi-Hitchin Correspondence in the Case λ=0 -- 1.7.1.6 OM0Z(H0∞)-Modules and C(w)-Modules with an Automorphism -- 1.7.2 The Correspondences in the General Case -- 1.7.2.1 Preliminary Consideration -- 1.7.2.2 Mini-complex Structure Corresponding to the Twistor Parameter λ -- 1.7.2.3 Another Coordinate System and the Compactification of Mλ -- 1.7.2.4 Mini-holomorphic Bundles Associated with Monopoles -- 1.7.2.5 Meromorphic Extension and Filtered Extension at Infinity -- 1.7.2.6 Kobayashi-Hitchin Correspondence of Periodic Monopoles of GCK Type -- 1.7.2.7 Difference Modules and OMλZ (Hλ∞)-Modules -- 1.8 Asymptotic Behaviour of Periodic Monopoles of GCK-Type -- 1.8.1 Setting -- 1.8.2 Decomposition of Mini-holomorphic Bundles -- 1.8.3 The Induced Higgs Bundles -- 1.8.3.1 Preliminary (1) -- 1.8.3.2 Preliminary (2) -- 1.8.3.3 The Induced Higgs Bundles -- 1.8.4 Asymptotic Orthogonality -- 1.8.5 Curvature Decay -- 1.8.6 The Filtered Extension in the Case λ=0 -- 1.8.7 The Filtered Extension for General λ -- 1.8.7.1 Ramified Covering Space -- 1.8.7.2 Approximation -- 1.8.7.3 Formal Completion of Asymptotic Harmonic Bundles at Infinity -- 1.8.7.4 The Formal Structure of PhEλ at Infinity -- 2 Preliminaries -- 2.1 Outline of This Chapter -- 2.2 Mini-Complex Structures on 3-Manifolds -- 2.2.1 Mini-Holomorphic Functions on RC -- 2.2.2 Mini-Complex Structure on Three-Dimensional Manifolds -- 2.2.3 Tangent Bundles -- 2.2.4 Cotangent Bundles -- 2.2.5 Meromorphic Functions -- 2.3 Mini-Holomorphic Bundles -- 2.3.1 Mini-Holomorphic Bundles -- 2.3.2 Metrics and the Induced Operators -- 2.3.3 Splittings -- 2.3.4 Scattering Maps -- 2.3.5 Dirac Type Singularity of Mini-Holomorphic Bundles -- 2.3.6 Kronheimer Resolution of Dirac Type Singularity -- 2.3.7 Precise Description of Dirac Type Singularities -- 2.3.8 Subbundles and Quotient Bundles.
2.3.9 Basic Functoriality -- 2.4 Monopoles -- 2.4.1 Monopoles and Mini-Holomorphic Bundles -- 2.4.2 Euclidean Monopoles -- 2.4.3 Dirac Type Singularity -- 2.4.3.1 Dirac Monopoles (Examples) -- 2.4.4 Basic Functoriality -- 2.5 Dimensional Reduction from 4D to 3D -- 2.5.1 Instantons Induced by Monopoles -- 2.5.2 Holomorphic Bundles and Mini-Holomorphic Bundles -- 2.6 Dimensional Reduction from 3D to 2D -- 2.6.1 Monopoles Induced by Harmonic Bundles -- 2.6.2 Mini-Holomorphic Bundles Induced by Holomorphic Bundles with a Higgs Field -- 2.6.3 Mini-Holomorphic Sections and Monodromy -- 2.6.4 Appendix: Monopoles as Harmonic Bundles of Infinite Rank -- 2.7 Twistor Families of Mini-Complex Structures on RC and (R/TZ)C -- 2.7.1 Preliminary -- 2.7.2 Spaces -- 2.7.3 Twistor Family of Complex Structures -- 2.7.4 Family of Mini-Complex Structures -- 2.7.5 The Mini-Complex Coordinate System (t0,β0) -- 2.7.6 The Mini-Complex Coordinate System (t1,β1) -- 2.7.7 Coordinate Change -- 2.7.8 Compactification -- 2.7.9 Mini-Holomorphic Bundles Associated with Monopoles -- 2.7.9.1 Compatibility with the Dimensional Reduction from 4D to 3D -- 2.8 OMλ-Modules and λ-Connections -- 2.8.1 Dimensional Reduction from OMλ-Modules to λ-Flat Bundles -- 2.8.1.1 Setting -- 2.8.1.2 Some Vector Fields and Forms -- 2.8.1.3 A General Equivalence -- 2.8.1.4 Mini-Holomorphic Bundles and Flat λ-Connections -- 2.8.1.5 λ-Flat Bundles of Infinite Rank -- 2.8.1.6 Remark -- 2.8.2 Comparison of Some Induced Operators -- 2.8.2.1 Comparison of Mini-Holomorphic Bundles Induced by Harmonic Bundles -- 2.8.3 OMλ-Modules and λ-Connections -- 2.8.3.1 Setting -- 2.8.3.2 A General Equivalence -- 2.8.3.3 Mini-Holomorphic Bundles and Meromorphic Flat λ-Connections -- 2.8.3.4 Another Description of the Construction -- 2.9 Curvatures of Mini-Holomorphic Bundles with Metric on Mλ.
2.9.1 Contraction of Curvature and Analytic Degree -- 2.9.2 Chern-Weil Formula -- 2.9.3 Another Description of G(h) -- 2.9.4 Change of Metrics -- 2.9.5 Relation with λ-Connections -- 2.9.5.1 λ-Flat Bundles of Infinite Rank with a Harmonic Metric -- 2.9.5.2 Remark -- 2.9.6 Dimensional Reduction of Kronheimer -- 2.9.7 Appendix: Ambiguity of the Choice of a Splitting -- 2.10 Difference Modules and OMλZ(Hλ∞)-Modules -- 2.10.1 Difference Modules with Parabolic Structure at Finite Place -- 2.10.2 Construction of Difference Modules from OMλZ(Hλ∞)-Modules -- 2.10.3 Construction of OMλZ(Hλ)-Modules from Difference Modules -- 2.10.4 Appendix: Mellin Transform and Parabolic Structures at Finite Place -- 2.10.4.1 Mellin Transform -- 2.10.4.2 Algebraic Nahm Transform for Filtered λ-Flat Bundles (Special Case) -- 2.11 Filtered Prolongation of Acceptable Bundles -- 2.11.1 Filtered Bundles on a Neighbourhood of 0 in C -- 2.11.1.1 G-Equivariance -- 2.11.1.2 Subbundles, Quotient and Splitting -- 2.11.1.3 Basic Functoriality -- 2.11.1.4 Pull Back -- 2.11.1.5 Push-Forward -- 2.11.1.6 Descent -- 2.11.1.7 Some Examples -- 2.11.2 Acceptable Bundles on a Punctured Disc -- 2.11.2.1 Basic Functoriality -- 2.11.2.2 Pull Back and Descent -- 2.11.3 Global Case -- 2.11.3.1 Filtered Bundles -- 2.11.3.2 Acceptable Bundles -- 3 Formal Difference Modules and Good Parabolic Structure -- 3.1 Outline of This Chapter -- 3.2 Formal Difference Modules -- 3.2.1 Formal Difference Modules of Level ≤1 -- 3.2.2 Formal Difference Modules of Pure Slope -- 3.2.3 Slope Decomposition of Formal Difference Modules -- 3.3 Good Filtered Bundles of Formal Difference Modules -- 3.3.1 Filtered Bundles over C((yq-1))-Modules -- 3.3.1.1 G-Equivariance -- 3.3.1.2 Submodules, Quotient Modules and Splittings -- 3.3.1.3 Basic Functoriality -- 3.3.1.4 Pull Back -- 3.3.1.5 Push-Forward -- 3.3.1.6 Descent.
3.3.2 Good Filtered Bundles over Formal Difference Modules -- 3.3.3 The Induced Endomorphisms on the Graded Pieces -- 3.4 Geometrization of Formal Difference Modules -- 3.4.1 Ringed Spaces -- 3.4.2 Some Formal Spaces -- 3.4.3 Difference Modules and OH∞,q(H∞,q)-Modules -- 3.4.4 Lattices and the Induced Local Systems -- 3.5 Filtered Bundles in the Formal Case -- 3.5.1 Pull Back and Descent of OH∞,p(H∞,p)-Modules -- 3.5.2 Filtered Bundles -- 3.5.2.1 Subbundles and Quotient Bundles -- 3.5.2.2 Basic Functoriality -- 3.5.2.3 Pull Back -- 3.5.2.4 Push-Forward -- 3.5.2.5 Descent -- 3.5.3 Basic Filtered Objects with Pure Slope -- 3.5.4 Good Filtered Bundles over OH∞,q(H∞,q)-Modules with Level ≤1 -- 3.5.5 Good Filtered Bundles over OH∞,q(H∞,q)-Modules -- 3.5.5.1 An Equivalence -- 3.5.5.2 Some Properties -- 3.5.6 Global Lattices on the Covering Space -- 3.5.7 Local Lattices -- 3.5.8 Complement for Good Filtered Bundles with Level ≤1 -- 3.6 Formal Difference Modules of Level ≤1 and Formal λ-Connections -- 3.6.1 Formal λ-Connections -- 3.6.2 Some Sheaves of Algebras on H∞,q -- 3.6.3 From Formal λ-Connections to Formal Difference Modules -- 3.6.4 Equivalence -- 3.6.4.1 Simpler Cases of Proposition 3.6.8 -- 3.6.5 Example 1 -- 3.6.5.1 -- 3.6.5.2 -- 3.6.6 Example 2 -- 3.6.6.1 -- 3.6.6.2 -- 3.6.7 Comparison of Good Filtered Bundles -- 3.6.8 Comparison of the Associated Graded Pieces -- 3.6.9 Some Functoriality -- 3.7 Appendix: Pull Back and Descent in the R-Direction -- 3.7.1 Examples -- 4 Filtered Bundles -- 4.1 Outline of This Chapter -- 4.2 Filtered Bundles in the Global Case -- 4.2.1 Subbundles and Quotient Bundles -- 4.2.2 Degree and Slope -- 4.2.3 Stability Condition -- 4.2.4 Good Filtered Bundles of Dirac Type and Parabolic Difference Modules -- 4.2.4.1 Polystable Parabolic Difference Modules -- 4.2.4.2 Equivalence -- 4.3 Filtered Bundles on Ramified Coverings.
4.3.1 The Case λ=0.
Record Nr. UNISA-996466416503316
Mochizuki Takuro <1972->  
Cham, Switzerland : , : Springer, , [2022]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
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Periodic monopoles and difference modules / / Takuro Mochizuki
Periodic monopoles and difference modules / / Takuro Mochizuki
Autore Mochizuki Takuro <1972->
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2022]
Descrizione fisica 1 online resource (336 pages)
Disciplina 516.36
Collana Lecture Notes in Mathematics
Soggetto topico Geometry, Differential
Geometria diferencial
Soggetto genere / forma Llibres electrònics
ISBN 9783030945008
9783030944995
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Preface -- Acknowledgements -- Contents -- 1 Introduction -- 1.1 Background and Motivation -- 1.2 Monopoles of GCK-Type -- 1.3 Previous Works on Monopoles and Algebraic Objects -- 1.3.1 SU(2)-Monopoles with Finite Energy on R3 -- 1.3.2 The Correspondence due to Charbonneau and Hurtubise -- 1.3.3 Remark -- 1.4 Review of the Kobayashi-Hitchin Correspondences for λ-Flat Bundles -- 1.4.1 Harmonic Bundles and Their Underlying λ-Flat Bundles -- 1.4.2 Kobayashi-Hitchin Correspondences in the Smooth Case -- 1.4.3 Tame Harmonic Bundles and Regular Filtered λ-Flat Bundles -- 1.4.4 Wild Harmonic Bundles and Good Filtered λ-Flat Bundles -- 1.5 Equivariant Instantons and the Underlying Holomorphic Objects -- 1.5.1 Instantons and the Underlying Holomorphic Bundles -- 1.5.2 Instantons and Harmonic Bundles -- 1.5.3 Instantons and Monopoles -- 1.5.4 Instantons and Monopoles as Harmonic Bundles of Infinite Rank -- 1.5.4.1 Instantons as Harmonic Bundles of Infinite Rank -- 1.5.4.2 The Underlying λ-Flat Bundles of Infinite Rank -- 1.5.4.3 Monopoles as Harmonic Bundles of Infinite Rank -- 1.6 Difference Modules with Parabolic Structure -- 1.6.1 Difference Modules -- 1.6.2 Parabolic Structure of Difference Modules at Finite Place -- 1.6.3 Good Parabolic Structure at ∞ -- 1.6.4 Parabolic Difference Modules -- 1.6.5 Degree and Stability Condition -- 1.6.6 Easy Examples of Stable Parabolic Difference Modules (1) -- 1.6.6.1 The Case Where (∞) Is Even -- 1.6.6.2 The Case Where (∞) Is Odd -- 1.6.7 Easy Examples of Stable Parabolic Difference Modules (2) -- 1.7 Kobayashi-Hitchin Correspondences for Periodic Monopoles -- 1.7.1 The Correspondence in the Case λ=0 -- 1.7.1.1 Mini-complex Structure -- 1.7.1.2 Mini-holomorphic Bundles Associated with Monopoles -- 1.7.1.3 Dirac Type Singularity -- 1.7.1.4 Meromorphic Extension and Filtered Extension at Infinity.
1.7.1.5 Kobayashi-Hitchin Correspondence in the Case λ=0 -- 1.7.1.6 OM0Z(H0∞)-Modules and C(w)-Modules with an Automorphism -- 1.7.2 The Correspondences in the General Case -- 1.7.2.1 Preliminary Consideration -- 1.7.2.2 Mini-complex Structure Corresponding to the Twistor Parameter λ -- 1.7.2.3 Another Coordinate System and the Compactification of Mλ -- 1.7.2.4 Mini-holomorphic Bundles Associated with Monopoles -- 1.7.2.5 Meromorphic Extension and Filtered Extension at Infinity -- 1.7.2.6 Kobayashi-Hitchin Correspondence of Periodic Monopoles of GCK Type -- 1.7.2.7 Difference Modules and OMλZ (Hλ∞)-Modules -- 1.8 Asymptotic Behaviour of Periodic Monopoles of GCK-Type -- 1.8.1 Setting -- 1.8.2 Decomposition of Mini-holomorphic Bundles -- 1.8.3 The Induced Higgs Bundles -- 1.8.3.1 Preliminary (1) -- 1.8.3.2 Preliminary (2) -- 1.8.3.3 The Induced Higgs Bundles -- 1.8.4 Asymptotic Orthogonality -- 1.8.5 Curvature Decay -- 1.8.6 The Filtered Extension in the Case λ=0 -- 1.8.7 The Filtered Extension for General λ -- 1.8.7.1 Ramified Covering Space -- 1.8.7.2 Approximation -- 1.8.7.3 Formal Completion of Asymptotic Harmonic Bundles at Infinity -- 1.8.7.4 The Formal Structure of PhEλ at Infinity -- 2 Preliminaries -- 2.1 Outline of This Chapter -- 2.2 Mini-Complex Structures on 3-Manifolds -- 2.2.1 Mini-Holomorphic Functions on RC -- 2.2.2 Mini-Complex Structure on Three-Dimensional Manifolds -- 2.2.3 Tangent Bundles -- 2.2.4 Cotangent Bundles -- 2.2.5 Meromorphic Functions -- 2.3 Mini-Holomorphic Bundles -- 2.3.1 Mini-Holomorphic Bundles -- 2.3.2 Metrics and the Induced Operators -- 2.3.3 Splittings -- 2.3.4 Scattering Maps -- 2.3.5 Dirac Type Singularity of Mini-Holomorphic Bundles -- 2.3.6 Kronheimer Resolution of Dirac Type Singularity -- 2.3.7 Precise Description of Dirac Type Singularities -- 2.3.8 Subbundles and Quotient Bundles.
2.3.9 Basic Functoriality -- 2.4 Monopoles -- 2.4.1 Monopoles and Mini-Holomorphic Bundles -- 2.4.2 Euclidean Monopoles -- 2.4.3 Dirac Type Singularity -- 2.4.3.1 Dirac Monopoles (Examples) -- 2.4.4 Basic Functoriality -- 2.5 Dimensional Reduction from 4D to 3D -- 2.5.1 Instantons Induced by Monopoles -- 2.5.2 Holomorphic Bundles and Mini-Holomorphic Bundles -- 2.6 Dimensional Reduction from 3D to 2D -- 2.6.1 Monopoles Induced by Harmonic Bundles -- 2.6.2 Mini-Holomorphic Bundles Induced by Holomorphic Bundles with a Higgs Field -- 2.6.3 Mini-Holomorphic Sections and Monodromy -- 2.6.4 Appendix: Monopoles as Harmonic Bundles of Infinite Rank -- 2.7 Twistor Families of Mini-Complex Structures on RC and (R/TZ)C -- 2.7.1 Preliminary -- 2.7.2 Spaces -- 2.7.3 Twistor Family of Complex Structures -- 2.7.4 Family of Mini-Complex Structures -- 2.7.5 The Mini-Complex Coordinate System (t0,β0) -- 2.7.6 The Mini-Complex Coordinate System (t1,β1) -- 2.7.7 Coordinate Change -- 2.7.8 Compactification -- 2.7.9 Mini-Holomorphic Bundles Associated with Monopoles -- 2.7.9.1 Compatibility with the Dimensional Reduction from 4D to 3D -- 2.8 OMλ-Modules and λ-Connections -- 2.8.1 Dimensional Reduction from OMλ-Modules to λ-Flat Bundles -- 2.8.1.1 Setting -- 2.8.1.2 Some Vector Fields and Forms -- 2.8.1.3 A General Equivalence -- 2.8.1.4 Mini-Holomorphic Bundles and Flat λ-Connections -- 2.8.1.5 λ-Flat Bundles of Infinite Rank -- 2.8.1.6 Remark -- 2.8.2 Comparison of Some Induced Operators -- 2.8.2.1 Comparison of Mini-Holomorphic Bundles Induced by Harmonic Bundles -- 2.8.3 OMλ-Modules and λ-Connections -- 2.8.3.1 Setting -- 2.8.3.2 A General Equivalence -- 2.8.3.3 Mini-Holomorphic Bundles and Meromorphic Flat λ-Connections -- 2.8.3.4 Another Description of the Construction -- 2.9 Curvatures of Mini-Holomorphic Bundles with Metric on Mλ.
2.9.1 Contraction of Curvature and Analytic Degree -- 2.9.2 Chern-Weil Formula -- 2.9.3 Another Description of G(h) -- 2.9.4 Change of Metrics -- 2.9.5 Relation with λ-Connections -- 2.9.5.1 λ-Flat Bundles of Infinite Rank with a Harmonic Metric -- 2.9.5.2 Remark -- 2.9.6 Dimensional Reduction of Kronheimer -- 2.9.7 Appendix: Ambiguity of the Choice of a Splitting -- 2.10 Difference Modules and OMλZ(Hλ∞)-Modules -- 2.10.1 Difference Modules with Parabolic Structure at Finite Place -- 2.10.2 Construction of Difference Modules from OMλZ(Hλ∞)-Modules -- 2.10.3 Construction of OMλZ(Hλ)-Modules from Difference Modules -- 2.10.4 Appendix: Mellin Transform and Parabolic Structures at Finite Place -- 2.10.4.1 Mellin Transform -- 2.10.4.2 Algebraic Nahm Transform for Filtered λ-Flat Bundles (Special Case) -- 2.11 Filtered Prolongation of Acceptable Bundles -- 2.11.1 Filtered Bundles on a Neighbourhood of 0 in C -- 2.11.1.1 G-Equivariance -- 2.11.1.2 Subbundles, Quotient and Splitting -- 2.11.1.3 Basic Functoriality -- 2.11.1.4 Pull Back -- 2.11.1.5 Push-Forward -- 2.11.1.6 Descent -- 2.11.1.7 Some Examples -- 2.11.2 Acceptable Bundles on a Punctured Disc -- 2.11.2.1 Basic Functoriality -- 2.11.2.2 Pull Back and Descent -- 2.11.3 Global Case -- 2.11.3.1 Filtered Bundles -- 2.11.3.2 Acceptable Bundles -- 3 Formal Difference Modules and Good Parabolic Structure -- 3.1 Outline of This Chapter -- 3.2 Formal Difference Modules -- 3.2.1 Formal Difference Modules of Level ≤1 -- 3.2.2 Formal Difference Modules of Pure Slope -- 3.2.3 Slope Decomposition of Formal Difference Modules -- 3.3 Good Filtered Bundles of Formal Difference Modules -- 3.3.1 Filtered Bundles over C((yq-1))-Modules -- 3.3.1.1 G-Equivariance -- 3.3.1.2 Submodules, Quotient Modules and Splittings -- 3.3.1.3 Basic Functoriality -- 3.3.1.4 Pull Back -- 3.3.1.5 Push-Forward -- 3.3.1.6 Descent.
3.3.2 Good Filtered Bundles over Formal Difference Modules -- 3.3.3 The Induced Endomorphisms on the Graded Pieces -- 3.4 Geometrization of Formal Difference Modules -- 3.4.1 Ringed Spaces -- 3.4.2 Some Formal Spaces -- 3.4.3 Difference Modules and OH∞,q(H∞,q)-Modules -- 3.4.4 Lattices and the Induced Local Systems -- 3.5 Filtered Bundles in the Formal Case -- 3.5.1 Pull Back and Descent of OH∞,p(H∞,p)-Modules -- 3.5.2 Filtered Bundles -- 3.5.2.1 Subbundles and Quotient Bundles -- 3.5.2.2 Basic Functoriality -- 3.5.2.3 Pull Back -- 3.5.2.4 Push-Forward -- 3.5.2.5 Descent -- 3.5.3 Basic Filtered Objects with Pure Slope -- 3.5.4 Good Filtered Bundles over OH∞,q(H∞,q)-Modules with Level ≤1 -- 3.5.5 Good Filtered Bundles over OH∞,q(H∞,q)-Modules -- 3.5.5.1 An Equivalence -- 3.5.5.2 Some Properties -- 3.5.6 Global Lattices on the Covering Space -- 3.5.7 Local Lattices -- 3.5.8 Complement for Good Filtered Bundles with Level ≤1 -- 3.6 Formal Difference Modules of Level ≤1 and Formal λ-Connections -- 3.6.1 Formal λ-Connections -- 3.6.2 Some Sheaves of Algebras on H∞,q -- 3.6.3 From Formal λ-Connections to Formal Difference Modules -- 3.6.4 Equivalence -- 3.6.4.1 Simpler Cases of Proposition 3.6.8 -- 3.6.5 Example 1 -- 3.6.5.1 -- 3.6.5.2 -- 3.6.6 Example 2 -- 3.6.6.1 -- 3.6.6.2 -- 3.6.7 Comparison of Good Filtered Bundles -- 3.6.8 Comparison of the Associated Graded Pieces -- 3.6.9 Some Functoriality -- 3.7 Appendix: Pull Back and Descent in the R-Direction -- 3.7.1 Examples -- 4 Filtered Bundles -- 4.1 Outline of This Chapter -- 4.2 Filtered Bundles in the Global Case -- 4.2.1 Subbundles and Quotient Bundles -- 4.2.2 Degree and Slope -- 4.2.3 Stability Condition -- 4.2.4 Good Filtered Bundles of Dirac Type and Parabolic Difference Modules -- 4.2.4.1 Polystable Parabolic Difference Modules -- 4.2.4.2 Equivalence -- 4.3 Filtered Bundles on Ramified Coverings.
4.3.1 The Case λ=0.
Record Nr. UNINA-9910548172003321
Mochizuki Takuro <1972->  
Cham, Switzerland : , : Springer, , [2022]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui