Fields Academy Shared Graduate Course: Class Field Theory
Description
Instructor: Professor Ila Varma, University of Toronto
Course Dates: September 10th - December 4th, 2024
Mid-Semester Break: October 28th - November 1st, 2024
Lecture Times: Tuesdays, 2:00 PM - 4:00 PM (ET) | Wednesday, 3:00 PM - 4:00 PM (ET)
Office Hours: Wednesdays, 2:00 PM - 3:00 PM (ET)
Registration Fee: Free
Capacity Limit: N/A
Format: Online via Zoom (some weeks hybrid at UofT)
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.
For more information on course description, evaluation method (e.g., weight distribution), and course expectations, please refer to the course website: https://www.math.toronto.edu/~ila/mat1210f2024.html.
