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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 | ||
| ||
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 | ||
| ||
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 | ||
| ||
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 | ||
| ||
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 | ||
| ||
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 | ||
| ||
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 | 3-540-93913-X |
| 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 | ||
| ||
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->
|
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| 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 | ||
| ||