Algebraic Functions and Projective Curves Book

	Preface
	Introduction
1	Background	1
1.1	Valuations	1
1.2	Completions	16
1.3	Differential Forms	24
1.4	Residues	30
2	Function Fields	40
2.1	Divisors and Adeles	40
2.2	Weil Differentials	47
2.3	Elliptic Functions	52
2.4	Geometric Function Fields	54
2.5	Residues and Duality	58
3	Finite Extensions	68
3.1	Norm and Conorm	69
3.2	Scalar Extensions	72
3.3	The Different	75
3.4	Singular Prime Divisors	82
3.5	Galois Extensions	89
3.6	Hyperelliptic Functions	93
4	Projective Curves	103
4.1	Projective Varieties	103
4.2	Maps to P[superscript n]	108
4.3	Projective Embeddings	114
4.4	Weierstrass Points	122
4.5	Plane Curves	136
5	Zeta Functions	150
5.1	The Euler Product	151
5.2	The Functional Equation	154
5.3	The Riemann Hypothesis	156
A	Elementary Field Theory	164
	References	175
	Index	177