Algebraic number theory II:

This course is to give an introduction to class field theory

from cohomological point of view. We basically follow the book:

Algebraic Number theory, edited by Cassels and Frohlich.

Syllabus:

Week 1 Local fields I Absolute values
Week 2 Local fields II Hensel's lemma, unramified extensions
Week 3 Global fields Adeles and ideles
Week 4 Local class field theory I Lubin-Tate theory
Week 5 Group cohomology I Generalities
Week 6 Group cohomology II Tate's theorem
Week 7 Local class field theory II Construction of local reciprocity law
Week 8 Local class field theory III Kronecker-Weber theorem
Week 9 Local class field theory IV Existence theorem
Week 10 Student presentation  
Week 11 Local class field theory V Ramification theory
Week 12 Student presentation Brauer group and division algebras
Week 13 Global class field theory I Introduction
Week 14 Global class field theory II First inequality
Week 15 Global class field theory III Second inequality
Week 16    
Week 17