Spring 2024
Math 223b: Class Field Theory
E-mail: tayou@math.harvard.edu ,
Office: Science Center 238.
E-mail: jianqiaoxia@math.harvard.edu ,
Office: Science Center 421g.
Schedule:
- Meeting times: Tuesday-Thursday 09:00 AM-10:15 AM.
- Room: Science Ctr 113.
- First meeting: Tuesday, January 23rd.
- Office hours: Friday, from 3PM to 4:30PM or by appointment, in Science Center 238.
Further details will be posted on Canvas.
Syllabus:
This course is a continuation of Math 223A. We will talk about global class field theory. This can be seen as a vast generalization of quadratic reciprocity laws. We will talk about analytic methods in algebraic number theory, Brauer groups and central simple algebras. If time permits, we will give a brief introduction to the Langlands program.
Recommended books:
The main references will be:
- Jean-Pierre Serre,"Local Fields".
- Jürgen Neukirch, "Algebraic Number Theory".
For more advanced reading and exercises, I recommend the following books:
- Gerald J.Janusz, "Algebraic Number fields".
- Jürgen Neukirch, "Cohomology of Number Fields".
- Daniel Bump et al., " An Introduction to the Langlands Program".
Prerequisites:
Math 122-123 (Algebra I-II) or equivalent. Math 223a.
Grading:
For students requiring a grade, homework will be assigned. The solutions can either be scanned or typed and uploaded on Canvas. Homework will count for at least 70% of the final grade. Late homework can only be accepted under special circumstances. Collaborative work on homework is accepted but you must write your own solution as well as the names of the collaborators. There will be a final paper which will count for 30% of the grade.