Student Number Theory Seminar

Theodore Hui, Cornell University

“Class Field Theory and its Applications”

Class Field Theory is just like Galois Theory or the Fundamental Theorem of Algebra in the sense that the statements are useful and powerful in their own rights - you don’t really need to worry too much about their proofs before knowing how to apply them.

In this talk, I will first state the main theorems of the local and global class field theory. Then I will answer the following two questions in full detail:

1. How to find all the degree 3 abelian extensions of Q13?
2. Given a square-free integer n, how to find the minimal m such that Q(√n) ⊂ Q(ζm)?

The methods for solving the general cases will almost follow immediately.

MC 5479