Preface.
Introduction
1 Background
1.1 Valuations
1.2 Completions
1.3 Differential Forms
1.4 Residues
1.5 Exercises
2 FunctionFields
2.1 Divisors and Adeles
2.2 Weil Differentials
2.3 Elliptic Functions
2.4 Geometric Function Fields
2.5 Residues and Duality
2.6 Exercises
3 FiniteExtensions
3.1 Norm and Conorm
3.2 Scalar Extensions
3.3 The Different
3.4 Singular Prime Divisors
3.5 Galois Extensions
3.6 Hypcrelliptic Functions
3.7 Exercises
4 ProjectiveCurves
4.1 Projective Varieties
4.2 Maps to Pn
4.3 Projective Embeddings
4.4 Weierstrass Points
4.5 Plane Curves
4.6 Exercises
5 ZetaFunctions
5.1 The Euler Product
5.2 The Functional Equation
5.3 The Riemann Hypothesis
5.4 Exercises
AElementary Field Theory
References
Index
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