Fields Academy Shared Graduate Course: Class Field Theory
Description
Instructor: Professor Ila Varma, University of Toronto
Course Description
This course will give an introduction to class field theory, the study of abelian extensions of number fields and p-adic fields, focusing on statements and examples such as the Kronecker-Weber Theorem. At the beginning, we will review inertia groups and decomposition groups, and we will use that foundation to introduce the Galois theory of local fields.
Textbooks:
- A. Sutherland, Number Theory Lecture Notes, MIT OpenCourseWare, 2021.
See full course here: https://www.math.utoronto.ca/~ila/mat1210f2023.html, including problem sets:
- N. Childress, Class Field Theory, Universitext, 2009.
- G.J. Janusz, Algebraic Number Fields, GSM, v.2, 1996.
(More logistical details are coming soon.)