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书名 p进Teichmuller理论基础(英文版)(精)/美国数学会经典影印系列
分类 科学技术-自然科学-数学
作者 (日)望月新一
出版社 高等教育出版社
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简介
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望月新一著的《p进Teichmuller理论基础(英文版)(精)》为p进双曲曲线及其模空间的单值化理论奠定了基础。一方面,这个理论将复双曲曲线及其模空间的Fuchs和Bers单值化推广到了非阿基米德情形,该理论在本书中简称为p进Teichmuller理论。另一方面,该理论可以看作是常阿贝尔簇及其模空间的Serre—Tate理论的相当精确的双曲模拟。
p进双曲曲线及其模空间的单值化理论始于作者先前的一些工作。从某种意义上说,本书是对先前工作的概括和延续。本书旨在填补所提出方法与在本科复分析课程中研究的双曲黎曼曲面的经典单值化之间的缺口。
介绍从p进伽罗瓦表示的角度对曲线模空间的一种系统化处理。
给出Serre—Tate理论的双曲曲线模拟。
建立Fuchs和Bers单值化理论的p进模拟。
提供p进Hodge理论的一个“非阿贝尔例子”的系统化处理。
目录
Table of Contents
Introduction
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 MTv-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
2.2.5. The Case of CM Elliptic Curves
2.2.6. The Third Real Dimension as the Probenius 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
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. Representability
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
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
1.4. Torally Crys-Stable Bundles of Arbitrary Positive Level
1.5. The Geometric Connectedness of ,
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
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. Atfineness Properties
2.1. A Trivialization of a Certain Line Bundle on n
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
0. Introduction
1. Explicit Computation in the Case
1.1. Irreducible Components of Degree Two
1.2. The Case of Radius
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
Pictorial Appendix
Chapter
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