Algebraic Number Theory

Lior Silberman (University of British Columbia)

Jan 1, 2024 — Apr 30, 2024

About the course

This will be a standard graduate number theory course. Topics will include:

  • Number fields, rings of integers, ideals and unique factorization. Finiteness of the class group.
  • Valuations and completions; local fields.
  • Ramification theory, the different and discriminant.
  • Geometry of numbers: Dirichlet’s Unit Theorem. and discriminant bounds.
  • Other topics if time permits

The main pre-requisites are basic algebra (rings and fields, rings of polynomials, unique factorization in Euclidean\ndomains), basic number theory (modular arithemtic, factorization into primes) and Galois Theory, but no specific courses are required.


This course is available for registration under the Western Dean's Agreement. To register, you must obtain the approval of the course instructor and you must complete the Western Dean's agreement form , using the details below. The completed form should be signed by your home institution department and school of graduate studies, then returned to the host institution of the course.

Enrollment Details

Course Name
Algebraic Number Theory
Jan 1, 2024 — Apr 30, 2024
Course Number
MATH 535
Section Number
Section Code


For help with completing the Western Dean’s agreement form, please contact the graduate student program coordinator at your institution. For more information about the agreement, please see the Western Dean's Agreement website

Other Course Details

Lecture Schedule

Lectures will take place every Wednesday and Friday from 10:00am-11:30am (Pacific Time).

Remote Access

Lectures will be shared via zoom. Students will need to have installed the zoom app on their desktop/laptop.