algebraic functions and projective curves

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1、AlgebraicFunctionsandProjectiveCurvesDavidM.GoldschmidtNovember19,2001iic2001DavidM.GoldschmidtContentsPreface........................................vIntroduction.....................................v1Background11.1Valuations...................................11.2Completions......................

2、............171.3DifferentialForms...............................251.4Residues....................................321.5Exercises...................................392FunctionFields432.1DivisorsandAdeles..............................432.2WeilDifferentials...............................512.3Elliptic

3、Functions...............................552.4GeometricFunctionFields..........................572.5ResiduesandDuality.............................622.6Exercises...................................693FiniteExtensions733.1NormandCo-Norm..............................743.2ScalarExtensions..............

4、.................773.3TheDifferent.................................813.4SingularPrimeDivisors............................883.5GaloisExtensions...............................953.6HyperellipticFunctions............................993.7Exercises...................................1064ProjectiveCurves1

5、094.1Projectivevarieties..............................1094.2MapstoPn..................................1134.3ProjectiveEmbeddings............................1204.4WeierstrassPoints...............................1294.5PlaneCurves.................................142iiiCONTENTSCONTENTS4.6Exercises....

6、...............................1545ZetaFunctions1575.1TheEulerProduct...............................1585.2TheFunctionalEquation...........................1615.3TheRiemannHypothesis...........................1635.4Exercises...................................168AFieldExtensions171Bibliography.......

7、.............................181Index........................................183ivc2001DavidM.GoldschmidtPrefaceThisbookgrewoutofasetofnotesforaseriesoflecturesIorginallygaveattheCenterforCommunicationsResearchan