Foundations of p-adic Teichmüller theory:
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Mathematical Society
[1999]
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| Schriftenreihe: | American Mathematical Society: AMS/IP studies in advanced mathematics
volume 11 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xii, 529 Seiten Illustrationen |
| ISBN: | 0821811908 |
Internformat
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| 100 | 1 | |a Mochizuki, Shinichi |e Verfasser |0 (DE-588)1258834995 |4 aut | |
| 245 | 1 | 0 | |a Foundations of p-adic Teichmüller theory |c Shinichi Mochizuki |
| 264 | 1 | |a Providence, RI |b American Mathematical Society |c [1999] | |
| 264 | 4 | |c © 1999 | |
| 300 | |a xii, 529 Seiten |b Illustrationen | ||
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| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a American Mathematical Society: AMS/IP studies in advanced mathematics |v volume 11 | |
| 650 | 7 | |a Teichmüller-ruimten |2 gtt | |
| 650 | 4 | |a Teichmüller spaces | |
| 650 | 4 | |a p-adic analysis | |
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Datensatz im Suchindex
| _version_ | 1804127468168151040 |
|---|---|
| adam_text | Table of Contents
Table of Contents vii
Introduction 1
§0. Motivation
§0.1. The Fuchsian Uniformization
§0.2. Reformulation in Terms of Metrics
§0.3. Reformulation in Terms of Indigenous Bundles
§0.4. Frobenius Invariance and Integrality
§0.5. The Canonical Real Analytic Trivialization of the
Schwarz Torsor
§0.6. The Frobenius Action on the Schwarz Torsor at the
Infinite Prime
§0.7. Review of the Case of Abelian Varieties
§0.8. Arithmetic Frobenius Venues
§0.9. The Classical Ordinary Theory
§0.10. Intrinsic Hodge Theory
§1. Overview of the Contents of the Present Book
§1.1. Major Themes
§1.2. Atoms, Molecules, and Nilcurves
§1.3. The MJ^-Object Point of View
§1.4. The Generalized Notion of a Frobenius Invariant
Indigenous Bundle
§1.5. The Generalized Ordinary Theory
§1.6. Geometrization
§1.7. The Canonical Galois Representation
§1.8. Ordinary Stable Bundles
§2. Open Problems
§2.1. Basic Questions
§2.2. Canonical Curves and Hyperbolic Geometry
§2.2.1. Review of Kleinian Groups
§2.2.2. Review of Three-Dimensional Hyperbolic
Geometry
§2.2.3. Rigidity and Density Results
§2.2.4. QF-Canonical Curves
vii
viii CONTENTS
§2.2.5. The Case of CM Elliptic Curves
§2.2.6. The Third Real Dimension as the Frobenius
Dimension
§2.3. Towards an Arithmetic Kodaira-Spencer Theory
§2.3.1. The Schwarz Torsor as Dual to the
Kodaira-Spencer Morphism
§2.3.2. Arithmetic Resolutions of the Schwarz Torsor
Chapter I: Crys-Stable Bundles 87
§0. Introduction
§1. Definitions and First Properties
§1.1. Notation Concerning the Underlying Curve
§1.2. Definition of a Crys-Stable Bundle
§1.3. Isomorphisms
§1.4. De Rham Cohomology
§2. Moduli
§2.1. Boundedness
§2.2. Definition of Various Functors
§2.3. Represent ability
§2.4. Radimmersions
§3. Further Structure
§3.1. Crystal in Algebraic Spaces
§3.2. Hodge Morphisms
§3.3. Clutching Behavior
§4. Torally Indigenous Bundles
§4.1. Definitions
§4.2. Explicit Computation of Monodromy
§4.3. Moduli and de Rham Cohomology
§4.4. Clutching Morphisms
§5. The Universal Torsor of Torally Indigenous Bundles
§5.1. Notation
§5.2. Computation
§5.3. The Case of Dimension One
Chapter II: Torally Crys-Stable Bundles in
Positive Characteristic 125
§0. Introduction
§1. The p-Curvature of a Torally Crys-Stable Bundle
§1.1. Terminology
§1.2. The p-Curvature at a Marked Point
§1.3. The Verschiebung Morphism
CONTENTS ix
§1.4. Torally Crys-Stable Bundles of Arbitrary Positive Level
§1.5. The Geometric Connectedness of JJpgr
§1.6. Degenerations of Torally Crys-Stable Bundles of
Positive Level
§2. Nilpotent Connections of Higher Order
§2.1. Higher Order Connections
§2.2. De Rham Cohomology Computations
§2.3. Versal Families at Infinity
§3. Mildly Spiked Bundles
§3.1. Definition and First Properties
§3.2. De Rham Cohomology Computations
§3.3. Deformation Theory
Chapter III: VF-Patterns 171
§0. Introduction
§1. The Moduli Stack Associated to a VF-Pattern
§1.1. Definition of a VF-Pattern
§1.2. Construction of Link Stacks
§1.3. The Stack Associated to a VF-Pattern
§2. Afflneness Properties
§2.1. A Trivialization of a Certain Line Bundle on J7gr
§2.2. Some Ampleness Results
§2.3. Affine Stacks
§2.4. Absolute Affineness
§2.5. The Connectedness of the Moduli Stack of Curves
Chapter IV: Construction of Examples 199
§0. Introduction
§1. Explicit Computation in the Case g=l; r=l; p=5
§1.1. Irreducible Components of Degree Two
§1.2. The Case of Radius 1
§1.3. Conclusions
§2. Higher Order Connections and Lubin-Tate Stacks
§2.1. The Projective Line Minus Three Points
§2.2. Elliptic Curves
§2.3. Lubin-Tate Stacks
§3. Anabelian Stacks
§3.1. Basic Definitions
§3.2. Nondormant Bundles on the Projective Line Minus
Three Points
§3.3. Explicit Construction of Spiked Data
x CONTENTS
Pictorial Appendix
Chapter V: Combinatorialization at Infinity of the Stack of
Nilcurves 229
§0. Introduction
§1. Statement of Main Results
§2. The Main Theorem
§2.1. The Aphilial Case
§2.2. Grafting on Dormant Atoms I: Virtual p-Curvatures
§2.3. Grafting on Dormant Atoms II: Deformation Theory
§2.4. Proof of the Main Theorem
§3. Examples
§3.1. Consequences in the Case (g,r) = (1,1)
§3.2. Explicit Computations
Pictorial Appendix
Chapter VI: The Stack of Quasi-Analytic Self-Isogenies .... 273
§0. Introduction
§1. Definition of the Stacks Qg r
§1.1. Epiperfect Schemes
§1.2. The Epiperfect Category
§1.3. Epiperfect Log Schemes
§1.4. The Definition of the Stack of Quasi-Analytic
Self-Isogenies
§2. Deformation and Degeneration Properties of the Stacks Qgr
§2.1. Lifting Properties of Q r
§2.2. Represent ability and Affineness Properties of ~Qgr
§2.3. Embeddings of g r
§2.4. The Lattice of Subobjects of Sw
Chapter VII: The Generalized Ordinary Theory 301
§0. Introduction
§1. The Il-Ordinary Locus
§1.1. The Frobenius Action on the Crystalline Cohomology
§1.2. Interpretation of the Condition of n-Ordinariness
§1.3. Systems of Canonical Modular Frobenius Liftings
§1.4. The Case of Elliptic Curves
§2. The Closure of the Binary Ordinary Locus
CONTENTS xi
§2.1. The Deperfection of the Closure
§2.2. The Differentials of the Deperfection
§2.3. The w-Closedness of the Binary Ordinary Locus
§3. Existence Results
§3.1. The Binary Case
§3.2. The Spiked Case
§3.3. Frobenius Liftings in the Very Ordinary Case
Pictorial Appendix
Chapter VIII: The Geometrization of Binary-Ordinary
Frobenius Liftings 345
§0. Introduction
§1. The General Framework
§1.1. Canonical Points
§1.2. The Meaning of Geometrization
§2. The Binary Case
§2.1. The Associated Differential Formal Group
§2.2. The Canonical Uniformizing p-divisible Group
§2.3. Multi-Uniformization by the Group Q
§2.4. Canonical Affine Coordinates
§2.5. Lubin-Tate Geometries
§2.6. Anabelian Geometries
§2.7. Deformation of the System of Frobenius Liftings
§3. Application to Curves and their Moduli
§3.1. Frobenius Liftings on the Moduli Stack
§3.2. Frobenius Liftings on the Universal Curve
Pictorial Appendix
Chapter IX: The Geometrization of Spiked Frobenius Liftings . 397
§0. Introduction
§1. The Formal Uniformizing MTV -Object
§1.1. The Objects in Question
§1.2. The Strong Portion of the Uniformization
§1.3. The Strong Portion of the Mantle
§1.4. The Renormalized Frobenius Pull-back of the Mantle
§1.5. Hodge Subspaces
§2. Associated Galois Representations
§2.1. The Strictly Weak Pair of Frobenius Liftings over the
Strong Perfection
§2.2. The Associated Non-affine Geometry
§2.3. Construction of the Galois Mantle: The Spiked Case
xii CONTENTS
§2.4. Discussion of the Resulting Spiked Geometry
§2.5. Construction of the Galois Mantle:
The Binary-Ordinary Case
§3. Application to Curves and their Moduli
§3.1. Frobenius Liftings on the Moduli Stack
§3.2. Frobenius Liftings on the Universal Curve
Pictorial Appendix
Chapter X: Representations of the Fundamental Group of
the Curve 463
§0. Introduction
§1. The Binary-Ordinary Case
§1.1. The Formal Ai;Fv-Object
§1.2. The Crystalline Induced Representation
§1.3. The Lubin-Tate Case
§1.4. Relation to the Profinite Teichmiiller Group
§2. The Very Ordinary Spiked Case
§2.1. The Formal .M^v-Object
§2.2. The Crystalline Induced Representation
§2.3. Relation to the Profinite Teichmiiller Group
§3. Conclusion
Appendix: Ordinary Stable Bundles on a Curve 493
§0. Introduction
§1. The Algebraic Theory
§1.1. Basic Definitions
§1.2. Moduli
§2. The Complex Theory
§2.1. Unitary Representations of the Fundamental Group
§2.2. The Kahler Approach
§3. The Ordinary p-adic Theory
§3.1. Crystals of Bundles with Connection
§3.2. Frobenius Actions
§3.3. The Ordinary Case
§3.4. Canonical Coordinates via the Weil Conjectures
Bibliography 519
Index 525
|
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| indexdate | 2024-07-09T18:33:49Z |
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| isbn | 0821811908 |
| language | English |
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| series | American Mathematical Society: AMS/IP studies in advanced mathematics |
| series2 | American Mathematical Society: AMS/IP studies in advanced mathematics |
| spelling | Mochizuki, Shinichi Verfasser (DE-588)1258834995 aut Foundations of p-adic Teichmüller theory Shinichi Mochizuki Providence, RI American Mathematical Society [1999] © 1999 xii, 529 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier American Mathematical Society: AMS/IP studies in advanced mathematics volume 11 Teichmüller-ruimten gtt Teichmüller spaces p-adic analysis Teichmüller-Raum (DE-588)4131425-6 gnd rswk-swf p-adische Analysis (DE-588)4252360-6 gnd rswk-swf Teichmüller-Raum (DE-588)4131425-6 s p-adische Analysis (DE-588)4252360-6 s DE-604 American Mathematical Society: AMS/IP studies in advanced mathematics volume 11 (DE-604)BV011103148 11 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008703124&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mochizuki, Shinichi Foundations of p-adic Teichmüller theory American Mathematical Society: AMS/IP studies in advanced mathematics Teichmüller-ruimten gtt Teichmüller spaces p-adic analysis Teichmüller-Raum (DE-588)4131425-6 gnd p-adische Analysis (DE-588)4252360-6 gnd |
| subject_GND | (DE-588)4131425-6 (DE-588)4252360-6 |
| title | Foundations of p-adic Teichmüller theory |
| title_auth | Foundations of p-adic Teichmüller theory |
| title_exact_search | Foundations of p-adic Teichmüller theory |
| title_full | Foundations of p-adic Teichmüller theory Shinichi Mochizuki |
| title_fullStr | Foundations of p-adic Teichmüller theory Shinichi Mochizuki |
| title_full_unstemmed | Foundations of p-adic Teichmüller theory Shinichi Mochizuki |
| title_short | Foundations of p-adic Teichmüller theory |
| title_sort | foundations of p adic teichmuller theory |
| topic | Teichmüller-ruimten gtt Teichmüller spaces p-adic analysis Teichmüller-Raum (DE-588)4131425-6 gnd p-adische Analysis (DE-588)4252360-6 gnd |
| topic_facet | Teichmüller-ruimten Teichmüller spaces p-adic analysis Teichmüller-Raum p-adische Analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008703124&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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