Student seminar in pure mathematics

Summary

The goal of the seminar is to learn the main aspects of class field theory, which aims at understanding abelian extensions of global fields in terms of the arithmetic of the field. The theory can also be seenas a first instance of the Langlands correspondence.

Content

Learning Prerequisites

Required courses

- Number theory I.a - Algebraic number theory

Recommended courses

- Algebra V - Galois Theory

- Rings and Modules

Learning Outcomes

By the end of the course, the student must be able to:

• Demonstrate their knowledge about global fields and class field theory

Transversal skills

• Make an oral presentation.
• Write a scientific or technical report.
• Access and evaluate appropriate sources of information.

Teaching methods

Each participant will lecture on a subject realted to class field theory. The lecture is complemented by the professor and exercise sessions.

Expected student activities

Prepare lectures, write lecture notes and solutions to exercises. Active participation during class and exercise sessions.

Assessment methods

The grade will depend on the participants oral presentation and written reports. There will be no final exam.

Resources

Bibliography

Class Field Theory by N. Childress

Class Field Theory by J.S. Milne

Algebraic Number Theory by J. W. S. Cassels and A. Frohlich

Moodle Link

• https://go.epfl.ch/MATH-563