18.786 | Spring 2016 | Graduate

Number Theory II: Class Field Theory


Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session


18.785 Number Theory I


This course is the continuation of 18.785 Number Theory I. It begins with an analysis of the quadratic case of Class Field Theory via Hilbert symbols, in order to give a more hands-on introduction to the ideas of Class Field Theory. More advanced topics in number theory are discussed in this course, such as Galois cohomology, proofs of class field theory, modular forms and automorphic forms, Galois representations, and quadratic forms.

Topics Covered

  • Quadratic extensions and Hilbert symbols
  • Homological algebra
  • Galois cohomology
  • Local class field theory via Tate cohomology
  • Brauer groups
  • Artin reciprocity and global class field theory

Textbook, References, and Lecture Notes

There is no required textbook; an annotated bibliography and lecture notes are provided.

Problem Sets

There are 7 weekly problem sets.


The grade will be determined by the problem set scores.

Course Info

As Taught In
Spring 2016
Learning Resource Types
Lecture Notes
Problem Sets