椭圆曲线

Preface to the Second EditionPreface to the First EditionAcknowledgments to the Second EditionAcknowledgments to the First 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 Mordell Conjecture 7 Real and Complex Points on EUipticCurves 8 The Elliptic Cu~e. Group Law on the Intersection of Two Quadrics in Projective.Three Space1 Elementary Properties of the Chord-Tangent Group Law on a Cubic Curve2 Plane Algebraic Curves 3 Elliptic Curves and Their Isomorphisms4 Families of Elliptic Curves and Geometric Propertiesof Torsion Points5 Reduction mod p and Torsion Points6 Proof of Mordell's Finite Generation Theorem.7 Galois Cohomology and Isomorphism Classification of Elliptic Curves over Arbitrary Fields8 Descent and Galois Cohomology9 Elliptic and Hypergeometric Functions10 Theta Functions11 Modular Functions.12 Endomorphisms of Elliptic Curves13 Elliptic Curves over Finite Fields14 Elliptic Curves over Local Fields15 Elliptic Curves over Global Fields and e-Adic Representations 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's Last Theorem19 Higher Dimensional Analogs of Elliptic Curves: Calabi-Yau Varieties20 Families of Elliptic CurvesAppendixReferencesList of NotationIndex

Preface to the Second EditionPreface to the First EditionAcknowledgments to the Second EditionAcknowledgments to the First 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 Mordell Conjecture 7 Real and Complex Points on EUipticCurves 8 The Elliptic Cu~e. Group Law on the Intersection of Two Quadrics in Projective.Three Space1 Elementary Properties of the Chord-Tangent Group Law on a Cubic Curve2 Plane Algebraic Curves 3 Elliptic Curves and Their Isomorphisms4 Families of Elliptic Curves and Geometric Propertiesof Torsion Points5 Reduction mod p and Torsion Points6 Proof of Mordell's Finite Generation Theorem.7 Galois Cohomology and Isomorphism Classification of Elliptic Curves over Arbitrary Fields8 Descent and Galois Cohomology9 Elliptic and Hypergeometric Functions10 Theta Functions11 Modular Functions.12 Endomorphisms of Elliptic Curves13 Elliptic Curves over Finite Fields14 Elliptic Curves over Local Fields15 Elliptic Curves over Global Fields and e-Adic Representations 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's Last Theorem19 Higher Dimensional Analogs of Elliptic Curves: Calabi-Yau Varieties20 Families of Elliptic CurvesAppendixReferencesList of NotationIndex
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