椭圆曲线算术（第2版）

图书标准信息

• 作者 希尔弗曼（JosephH.Silverman） 著
• 出版社 世界图书出版公司
• 出版时间 2011-07
• 版次 2
• ISBN 9787510037443
• 定价 59.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 513页
• 正文语种 英语

【内容简介】

IntheprefacetothefirsteditionofthisbookIremarkedonthepaucityofintro-ductorytextsdevotedtothearithmeticofellipticcurves.Thatunfortunatestateofaffairshaslongsincebeenremediedwiththepublicationofmanyvolumes,amongwhichmaybementionedbooksbyCassels.

【目录】

PrefacetotheSecondEdition
PrefacetotheFirstEdition
Introduction
CHAPTER1
AlgebraicVarieties
1.AffineVarieties
2.ProjectiveVarieties
3.MapsBetweenVarieties
Exercises

CHAPTER2
AlgebraicCurves
1.Curves
2.MapsBetweenCurves
3.Divisors
4.Differentials
5.TheRiemarm-RochTheorem
Exercises

CHAPTER3
TheGeometryofEllipticCurves
1.WeierstrassEquations
2.TheGroupLaw
3.EllipticCurves
4.Isogenies
5.TheInvariantDifferential
6.TheDualIsogeny
7.TheTateModule
8.TheWeilPairing
9.TheEndomorphismRing
10.TheAutomorphismGroup
Exercises

CHAPTER4
TheFormalGroupofanEllipticCurve
1.ExpansionAroundO
2.FormalGroups
3.GroupsAssociatedtoFormalGroups
4.TheInvariantDifferential
5.TheFormalLogarithm
6.FormalGroupsoverDiscreteValuationRings
7.FormalGroupsinCharacteristicp
Exercises

CHAPTER5
EllipticCurvesoverFiniteFields
1.NumberofRationalPoints
2.TheWeilConjectures
3.TheEndomorphismRing
4.CalculatingtheHasseInvariant
Exercises

CHAPTER6
EllipticCurvesoverC
1.EllipticIntegrals
2.EllipticFunctions
3.ConstructionofEllipticFunctions
4.MapsAnalyticandMapsAlgebraic
5.Uniformization
6.TheLefschetzPrinciple
Exercises

CHAPTER7
ComputingtheMordell-WeilGroup
CHAPTER8
AlgorithmicAspectsofEllipticCurves
APPENDIX