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关键词：
Elliptic Curves
书目信息
ISBN：
9780387954905（13位）
中图分类号：
O1
杜威分类号：
中文译名：
椭圆曲线
作者：
Husemoller
编者：
语种：
English
出版信息
出版社：
Springer
出版地：
出版年：
2004
版本：
2nd ed.
版本类型：
原版
丛书题名：
Graduate Texts in Mathematics Vol. 111
卷期：
文献信息
关键词：
Mathematics
前言：
摘要：
内容简介：
This book is an introduction to the theory of elliptic curves, ranging from its most elementary aspects to current research. The first part, which grew out of Tate's Haverford lectures, covers the elementary arithmetic theory of elliptic curves over the rationals. The next two chapters recast the arguments used in the proof of the Mordell theorem into the context of Galois cohomology and descent theory. This is followed by three chapters on the analytic theory of elliptic curves, including such topics as elliptic functions, theta functions, and modular functions. Next, the theory of endomorphisms and elliptic curves over infinite and local fields are discussed. The book concludes with three chapters surveying recent results in the arithmetic theory, especially those related to the conjecture of the Birch and Swinnerton-Dyer. This new edition contains three new chapters and the addition of two appendices by Stefan Theisen and Otto Forster. Dale Husemoeller is a member of t he faculty at the Max Planck Institute of Mathematics.
目次：
Introduction to Rational Points on Plane Curves.- Elementary Properties of the Chord-Tangent Group Law on a Cubic Curve.- Plane Algebraic Curves.- Factorial Rings and Elimination Theory.- Elliptic Curves and Their Isomorphism.- Families of Elliptic Curves and Geometric Properties of Torsion Points.- Reduction mod p and Torsion Points.- Proof of Mordell's Finite Generation Theorem.- Galois Cohomology and Isomorphism Classification of Elliptic Curves over Arbitrary Fields.- Descent and Galois Cohomology.- Elliptic and Hypergeometric Functions.- Theta Functions.- Modular Functions.- Endomorphisms of Elliptic Curves.- Elliptic Curves over Finite Fields.- Elliptic Curves over Local Fields.- Elliptic Curves over Global Fields and l-adic Representations.- L-Functions of an Elliptic Curve and Its Analytic Continuation.- Remarks on the Birch and Swinnerton-Dyer Conjecture.- Remarks on the Modular Curves Conjecture and Fermat's Last Theorem.- Higher Dimensional Analogs of Elliptic Curves: Calabi-Yau Varieties.- Families of Elliptic Curves.- Appendix I: Calabi-Yau Manifolds and String Theory.- Appendix II: Elliptic Curves in Algorithmic Number Theory.- Appendix III: Guide to the Exercises.
附录：
全文链接：
读者对象：
grad.
实体信息
页码：
装帧：
hard
尺寸：
其它形态细节：
其它信息
原价：
EUR
74.9500
原版ISBN：
其它ISBN：
图书特色：
书评：
扩展信息
Isbn：
0387954902
issue：
2006JC01
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