Theory of Function Fields
Math 524 - Fall 2023
Announcements
This page contains some information that can be helpful before you register for the course. After the registration, we will be using odtuclass. You should follow odtuclass and check your emails regularly for important announcements during the semester.
Course Objectives
There are many analogies between number theory over algebraic number fields and over algebraic function fields. Our goal is to elaborate on these connections. The content of the course is relatively simple and essential to modern number theory and algebraic geometry.
Lectures and Office Hour
The first meeting is on Wednesday, September 27 at 14:00 in M215. The lecture hours will be decided during this meeting.
Homeworks, Exams and Grading
Homeworks will be assigned on a regular basis and there will be 3-5 homework sets by the end of the semester. There will be one midterm and a final. The time and the method of each exam will be announced later.
Midterm, 30 points - around the 8th week.
Final, 30 points - during the final exam period.
Homework, 40 points.
Homework Policy: You should write your solutions on your own. You are allowed to consult other people's solutions for homework problems, but you must express everything in your own words. If you copy a solution, which is referred to as cheating, you will probably gain nothing and may encounter penalties.
Textbooks
Rosen, M., Number Theory in Function Fields.
Stichtenoth, H., Algebraic Function Fields and Codes. Second Edition.
Tentative Course Outline
Weeks 1-4: Elementary Number Theory in Fq[t]. Rosen 1-43.
Weeks 5-8: Foundations of the Theory of Algebraic Function Fields. Stichtenoth 1-40.
Weeks 9-11: Extensions of Algebraic Function Fields. Stichtenoth 67-119.
Weeks 12-14: Examples and Additional Topics.