Preface.
IntroductiOn
1 Background
1.1 Valuations
1.2 Completions.
1.3 Difrerential F0mls
1.4 Residues.
1.5 Exercises
2 Function Fields
2.1 Divisors and Adeles.
2.2 Weil Differentials
2.3 Elliptic FunctiOns
2.4 GeonleIric Function Fields
2.5 ResidIles and Duality
2.6 Excrcises
3 Finite Extenslons
3.1 Norm and Conorm
3.2 Scalar Extensions
3.3 The Different
3.4 SingularPrimeDiVisors
3.5 Galois Extensions
3.6 Hyperelliptic Functtions
3.7 Exercises
4 Projective Curves
4.1 Proiective Varieties
4.2 Maps to
4.3 Projective Embeddings
4.4 Weierstrass Points
4.5 Plane Curves
4.6 Exerciscs.
5 Zeta Functions
5.1 The Euler Product
5.2 The Functional Equation
5.3 The Riemann Hypothesis
5.4 Exercises
A Elementary Field Theory
References
Index