| 词条 | 椭圆曲线算术中的高等论题 |
| 释义 | 图书信息出版社: 世界图书出版公司; 第1版 (2010年1月1日) 外文书名: Advanced Topics in the Arithmetic of Elliptic Curves 平装: 525页 正文语种: 英语 开本: 24 ISBN: 7510004837, 9787510004834 条形码: 9787510004834 尺寸: 22 x 14.6 x 2.4 cm 重量: 721 g 内容简介《椭圆曲线算术中的高等论题(英文版)》内容简介：美国哈佛大学从1977年开始，曾多次举办”椭圆曲线” 班，《椭圆曲线算术中的高等论题(英文版)》作者是该讨论班成员之一。椭圆曲线是一个古老的数学课题，最近由于代数数论和代数几何等现代数学的进展，使它得到了新的活力。《椭圆曲线算术中的高等论题(英文版)》是以1986年版的《椭圆曲线的算术理论》为蓝本，但在知识体系上做了较大的改动形成了这不教程，讲述上也更加专业，但在思想上是作者前《椭圆曲线算术中的高等论题(英文版)》的延续。包括椭圆和模型函数；复乘方法；椭圆曲线；Néron模型；复域上的椭圆曲线等内容。每章末都配有大量习题。目次：椭圆和模型函数；复乘方法；椭圆曲线；Néron模型；复域上的椭圆曲线。 读者对象：适合数学专业的研究生和相关的科研人员。 目录Preface Computer Packages Acknowledgments Introduction CHAPTER Ⅰ Elliptic and Modular Functions The Modular Group The Modular Curve X(1) Modular Functions Uniformization and Fields of Moduli Elliptic Functions Revisited q-Expansions of Elliptic Functions q-Expansions of Modular Functions Jacobi's Product Formula for A(T) Hecke Operators Hecke Operators Acting on Modular Forms L-Series Attached to Modular Forms Exercises CHAPTER Ⅱ Complex Multiplication Complex Multiplication over C Rationality Questions Class Field Theory —— A Brief Review The Hilbert Class Field The Maximal Abelian Extension Integrality of j Cyclotomic Class Field Theory The Main Theorem of Complex Multiplication The Associated GrSssencharacter The L-Series Attached to a CM Elliptic Curve Exercises CHAPTER Ⅲ Elliptic Surfaces Elliptic Curves over Function Fields The Weak Mordell-Weil Theorem Elliptic Surfaces Heights on Elliptic Curves over Unction Fields Split Elliptic Surfaces and Sets of Bounded Height The Mordell-Weil Theorem for Fhnction Fields The Geometry of Algebraic Surfaces The Geometry of Fibered Surfaces The Geometry of Elliptic Surfaces Heights and Divisors on Varieties Specialization Theorems for Elliptic Surfaces Integral Points on Elliptic Curves over Function Fields Exercises CHAPTER Ⅳ The N6ron Model Group Varieties Schemes and S-Schemes Group Schemes Arithmetic Surfaces N6ron Models Existence of N6ron Models Intersection Theory, Minimal Models, and Blowing-Up The Special Fiber of a N6ron Model Tate's Algorithm to Compute the Special Fiber The Conductor of an Elliptic Curve Ogg's Formula Exercises CHAPTER Ⅴ Elliptic Curves over Complete Fields Elliptic Curves over C Elliptic Curves over R The Tate Curve The Tate Map Is Surjective Elliptic Curves over p-adic Fields Some Applications of p-adic Uniformization Exercises CHAPTER Ⅵ Local Height Functions Existence of Local Height Functions Local Decomposition of the Canonical Height Archimedean Absolute Values —— Explicit Formulas Non-Archimedean Absolute Values —— Explicit Formulas Exercises APPENDIX A Some Useful Tables Bernoulli Numbers and (2k) Fourier Coefficients of A(T) and j(T) Elliptic Curves over Q with Complex Multiplication Notes on Exercises References List of Notation Index |
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