椭圆曲线（第2版）

图书标准信息

• 作者 胡斯迈勒 著
• 出版社 世界图书出版公司
• 出版时间 2011-04
• 版次 2
• ISBN 9787510033032
• 定价 65.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 487页

【内容简介】

Dividesnaturallyintoseveralpartsaccordingtothelevelofthematerial,thebackgroundrequiredofthereader,andthestyleofpresentationwithrespecttodetailsofproofs.Forexample,thefirstpart,toChapter6,isundergraduateinlevel,thesecondpartrequiresabackgroundinGaloistheoryandthethirdsomecomplexanalysis,whilethelastparts,fromChapter12on,aremostlyatgraduatelevel.

【目录】

PrefacetotheSecondEdition
PrefacetotheFirstEdition
AcknowledgmentstotheSecondEdition
AcknowledgmentstotheFirstEdition
IntroductiontoRationalPointsonPlaneCurves
1RationalLinesintheProjectivePlane
2RationalPointsonConics
3Pythagoras,Diophantus,andFermat
4RationalCubicsandMordeli'sTheorem
5TheGroupLawonCubicCurvesandEllipticCurves
6RationalPointsonRationalCurves.FaltingsandtheMordellConjecture
7RealandComplexPointsonEUipticCurves
8TheEllipticCu~e.GroupLawontheIntersectionofTwoQuadricsin
Projective.ThreeSpace
1ElementaryPropertiesoftheChord-TangentGroupLawonaCubicCurve
2PlaneAlgebraicCurves
3EllipticCurvesandTheirIsomorphisms
4FamiliesofEllipticCurvesandGeometricPropertiesofTorsionPoints
5ReductionmodpandTorsionPoints
6ProofofMordell'sFiniteGenerationTheorem.
7GaloisCohomologyandIsomorphismClassificationofEllipticCurvesoverArbitraryFields
8DescentandGaloisCohomology
9EllipticandHypergeometricFunctions
10ThetaFunctions
11ModularFunctions.
12EndomorphismsofEllipticCurves
13EllipticCurvesoverFiniteFields
14EllipticCurvesoverLocalFields
15EllipticCurvesoverGlobalFieldsande-AdicRepresentations
16L.Functionofan,EllipticCurveandItsAnalyticContinuation
17RemarksontheBirchandSwinnerton-DyerConjecture
18RemarksontheModularEllipticCurvesConjectureandFermat'sLastTheorem
19HigherDimensionalAnalogsofEllipticCurves:Calabi-YauVarieties
20FamiliesofEllipticCurves
Appendix
References
ListofNotation
Index