Math 204C - Number Theory

Course description: This is the third in a string of three courses, which is an introduction to algebraic and analytic number theory. Part A treated the basics of number fields (their rings of integers, failure of unique factorization, class numbers, the Dirichlet unit theorem, splitting of primes, cyclotomic fields, and more). Part B focused on local fields and local properties of number fields (completions of number fields, finite extensions of local fields, ramification, different and discriminant, decomposition and inertia groups, basics of local class field theory). Part C will focus on zeta functions. The exact topics and order of presentation will be decided in consultation with the audience; the topics will most likely be a subset of the following.

Instructor: Kiran Kedlaya, kedlaya [at] ucsd [etcetera]. Office hours Tu 1-2 (note change), or by appointment, in APM 7202.

Lectures: MWF 1-1:50, in APM 7421; Tu 10-11, in APM 6402. See below for modifications to the schedule.

Textbook: No specific text. See lecture notes (and references) on the topics list.

Prerequisites: Math 204A or Math204B or equivalent with instructor's permission. I will be flexible about this, adapting the presentation based on the audience.

Homework: Informal. I will assign some exercises, but I do not expect to collect or grade them.

Final exam: None.

Grading: Let me know if you need a meaningful grade for this course.


Topics covered so far (with notes):