Preface
1.Algebraic Curves
1.1 The Riemann-Roch theorem
1.2 Residue of differential forms
1.3 Duality
1.4 The Riemann-Roch theorem for singular algebraic curves
1.5 Cartier divisors
2.Morphisms from Algebraic Curves to Algebraic Groups
2.1 Algebraic groups
2.2 Local symbols
2.3 Proof of Rosenlicht's theorem in characteristic 0
2.4 Proof of Rosenlicht's theorem in characteristic p
2.5 Local symbols for the additive group and the multiplicative group
3.Generalized Jacobians
3.1 Principal homogeneous spaces
3.2 Galois descent
3.3 Picard schemes and generalized Jacobians
3.4 Structures of generalized Jacobians
3.5 Extensions and torsors
4.Class Field Theory
4.1 The Lang isogeny
4.2 Coverings as pull backs of isogenies
4.3 Class field theory
4.4 Explicit reciprocity laws
Bibliography
Index
