橢圓曲線（第2版）

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《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.

Preface to the Second EditionPreface to the Fit EditionAcknowledgments to the Second EditionAcknowledgments to the Fit EditionIntroduction 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 MordellConjecture 7 Real and Complex Points on EUipticCurves 8 The Elliptic Cu~e. Group Law on the Inteection of Two Quadricsin Projective.Three Space1 Elementary Properties of the Chord-Tangent Group Law on a CubicCurve2 Plane Algebraic Curves 3 Elliptic Curves and Their Isomorphisms4 Families of Elliptic Curves and Geometric Propertiesof ToionPoints5 Reduction mod p and Toion Points6 Proof of Mordell's Finite Generation Theorem.7 Galois Cohomology and Isomorphism Classification of EllipticCurves over Arbitrary Fields8 Descent and Galois Cohomology9 Elliptic and Hypergeometric Functio10 Theta Functio11 Modular Functio.12 Endomorphisms of Elliptic Curves13 Elliptic Curves over Finite Fields14 Elliptic Curves over Local Fields15 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 Conjecture18 Remarks on the Modular Elliptic Curves Conjecture and Fermat'sLast Theorem19 Higher Dimeional Analogs of Elliptic Curves: Calabi-YauVarieties20 Families of Elliptic CurvesAppendixReferencesList of NotationIndex

橢圓曲線（第2版）

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