Course Meeting Times
Lectures: 2 sessions / week, 1.5 hours / session
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.
- 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.
There are 7 weekly problem sets.
The grade will be determined by the problem set scores.