189-596A: Class Field Theory

Professor: Henri Darmon

Class Times:
Mondays from 4:00-5:30, in BH 1234.
Tuesdays from 10:30-12:00, in BH 1104.
Make-up days: Fridays from 10:00-11:30, in BH 1214.

This rather complicated schedule, in which we manage to meet in three different time slots and in three different rooms each week, allows for an extra meeting day on Friday, in weeks where we need to make up lectures because of a cancelled Monday, and avoids conflicting with Sieves, Elliptic Curves, Etale Fundamental Groups, Compact Lie Groups, and sundry TA sessions.
Note in particular that we will meet this Friday, and not next Monday, the day of the Jewish New Year.

Course Blog:
The course blog keeps track of when the lectures are scheduled, and of what has been covered in each lecture. Check the blog if you have a doubt on when the lectures are scheduled.

Class Field Theory on the web:
Henri Darmon's web page: http://www.math.mcgill.ca/~darmon
Math 596A: http://www.math.mcgill.ca/~darmon/courses/cft/cft.html

Office hours:
Henri Darmon: by appointment, in BH 1111.

Textbooks:

1. J.S. Milne. Class field theory.

2. Jurgen Neukirch. Class field theory: the Bonn lectures.

3. Freydoon Shahidi. Class field theory.

4. Kiran Kedlaya. Notes on class field theory.

Syllabus:
This course will cover the statements and proofs of the main results of class field theory, following the references listed above, in decreasing order (roughly) of closeness. Details on the syllabus will be posted as we progress.

Grading Scheme :

40% Bi-weekly assignments. The bi-weekly assignments are an essential part of the course. You should plan to devote at least ten hours (and quite possibly more) to the assignments.

If you are stuck on a problem, you may seek out the help of one of your classmates. It is OK to work on the assignments in groups, although you should hand them in individually. Do not neglect the assignments: there is a strong correlation between the work you put into them and how well you will do in the final exam, and hence in the course.

The assignments are due on Mondays and will be graded and returned to you in the same week. Late assignments will not be accepted.

60% In-class final exam.
This exam will be given on Friday, December 7, from 10:00 AM to 1:00 PM, in BH 920.

The obligatory statements

McGill University values academic integrity. Therefore, all students must understand the meaning and consequences of cheating, plagiarism and other academic offences under the Code of Student Conduct and Disciplinary Procedures (see www.mcgill.ca/integrity for more information).

In accord with McGill University's Charter of Students' Rights, students in this course have the right to submit in English or in French any written work that is to be graded.

In the event of extraordinary circumstances beyond the University's control, the content and/or evaluation scheme in this course is subject to change.