Holdings: Foundations of p-adic Teichmüller theory

Foundations of p-adic Teichmüller theory:

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Bibliographic Details
Main Author:	Mochizuki, Shinichi (Author)
Format:	Book
Language:	English
Published:	Providence, RI American Mathematical Society [1999]
Series:	American Mathematical Society: AMS/IP studies in advanced mathematics volume 11
Subjects:	Teichmüller-ruimten Teichmüller spaces p-adic analysis Teichmüller-Raum p-adische Analysis
Online Access:	Inhaltsverzeichnis
Physical Description:	xii, 529 Seiten Illustrationen
ISBN:	0821811908

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MARC


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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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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
volume_link	(DE-604)BV011103148
work_keys_str_mv	AT mochizukishinichi foundationsofpadicteichmullertheory

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