Algebraic number theory II

Infinite Galois theory......Page 3 Projective and inductive limits......Page 10 Cohomology of groups and pro-finite groups......Page 16 Basics about modules and homological Algebra......Page 22 Applications to group cohomology......Page 32 Hilbert 90 and Kummer theory......Page 42 Properties of group cohomology......Page 49 Tate cohomology for finite groups......Page 54 Cohomology of cyclic groups......Page 57 The cup product......Page 64 The corestriction......Page 71 Local class field theory I......Page 76 Three Theorems of Tate......Page 81 Abstract class field theory......Page 84 Local class field theory II......Page 92 Local class field theory III......Page 95 Global class field theory I......Page 98 Global class field theory II......Page 102 Global class field theory III......Page 108 Global class field theory IV......Page 113