橢圓曲線

內(nèi)容概要

《橢圓曲線(第2版)》(作者胡斯邁勒)divides naturally
into several parts according to the level of the material,the
background required of the reader, and the style of presentation
with respect to details of proofs. For example, the first part, to
Chapter 6, is undergraduate in level,the second part requires a
background in Galois theory and the third some complex analysis,
while the last parts, from Chapter 12 on, are mostly at graduate
level.

書(shū)籍目錄

Preface to the Second Edition
Preface to the Fit Edition
Acknowledgments to the Second Edition
Acknowledgments to the Fit Edition
Introduction to Rational Points on Plane Curves
 i Rational Lines in the Projective Plane
 2 Rational Points on Conics
 3 Pythagoras, Diophantus, and Fermat
 4 Rational Cubics and Mordeli's Theorem
 5 The Group Law on Cubic Curves and Elliptic Curves
 6 Rational Points on Rational Curves. Faltings and the Mordell
Conjecture
 7 Real and Complex Points on EUipticCurves
 8 The Elliptic Cu~e. Group Law on the Inteection of Two Quadrics
in Projective.Three Space
1 Elementary Properties of the Chord-Tangent Group Law on a Cubic
Curve
2 Plane Algebraic Curves 
3 Elliptic Curves and Their Isomorphisms
4 Families of Elliptic Curves and Geometric Propertiesof Toion
Points
5 Reduction mod p and Toion Points
6 Proof of Mordell's Finite Generation Theorem.
7 Galois Cohomology and Isomorphism Classification of Elliptic
Curves over Arbitrary Fields
8 Descent and Galois Cohomology
9 Elliptic and Hypergeometric Functio
10 Theta Functio
11 Modular Functio.
12 Endomorphisms of Elliptic Curves
13 Elliptic Curves over Finite Fields
14 Elliptic Curves over Local Fields
15 Elliptic Curves over Global Fields and e-Adic Representatio 
16 L.Function of an,Elliptic Curve and Its Analytic Continuation 
17 Remarks on the Birch and Swinnerton-Dyer Conjecture
18 Remarks on the Modular Elliptic Curves Conjecture and Fermat's
Last Theorem
19 Higher Dimeional Analogs of Elliptic Curves: Calabi-Yau
Varieties
20 Families of Elliptic Curves
Appendix
References
List of Notation
Index

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