Linear algebraic groups

Summary

The aim of the course is to give an introduction to linear algebraic groups and to give an insight into a beautiful subject that combines algebraic geometry with group theory.

Content

Keywords

algebraic groups

group actions on algebraic varieties

Lie algebra

algebraic geometry

group theory

Learning Prerequisites

Required courses

at least one introductory course in algebraic geometry

Recommended courses

courses in group theory, Lie theory, and algebraic geometry

Learning Outcomes

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

• State the most important notions and results
• Construct examples
• Prove basic results in the theory
• Express your mathematical thoughts orally

Teaching methods

Lectures and exercises

Expected student activities

Attending the course, doing the weekly assignments, participating actively in the course and the exercise classes.

Assessment methods

There will be a final oral exam. Part of the grade might be based upon student presentation of some course material, quizes, or corrected written homework assignments.

Dans le cas de l'art. 3 al. 5 du Règlement de section, l'enseignant décide de la forme de l'examen qu'il communique aux étudiants concernés.

Supervision

Resources

Bibliography

Algebraic Transformation Groups - an Introduction, H. Kraft, manuscript on the website of the author

Linear Algebraic Groups, J. Humphreys, Springer

Linear Algebraic Groups, T. Springer, Birkhauser

Linear Algebraic Groups, A. Borel, Springer

Linear algebraic groups and finite groups of Lie type, G. Malle and D. Testerman, CUP

Références suggérées par la bibliothèque

• Linear Algebraic Groups / Borel
• Linear algebraic groups and finite groups of Lie type / Malle & Testerman
• Algebraic Transformation Groups / Kraft
• Linear Algebraic Groups / Springer
• Linear Algebraic Groups / Humphreys

Moodle Link

• https://go.epfl.ch/MATH-479