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