Linear algebraic groups
MATH-479 / 5 crédits
Enseignant:
Langue: Anglais
Remark: Pas donné en 2024-25
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
First definitions and properties, morphisms, Jordan decomposition, tangent space, commutative linear algebraic groups, tori, unipotent groups, the Lie algebra of a linear algebraic group, group actions on algebraic varieties, invariants and quotients, Hilbert's finiteness theorem.
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
Office hours | Yes |
Assistants | Yes |
Forum | Yes |
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
Dans les plans d'études
- Semestre: Printemps
- Forme de l'examen: Oral (session d'été)
- Matière examinée: Linear algebraic groups
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Type: optionnel
- Semestre: Printemps
- Forme de l'examen: Oral (session d'été)
- Matière examinée: Linear algebraic groups
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Type: optionnel
- Semestre: Printemps
- Forme de l'examen: Oral (session d'été)
- Matière examinée: Linear algebraic groups
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Type: optionnel
Semaine de référence
Lu | Ma | Me | Je | Ve | |
8-9 | |||||
9-10 | |||||
10-11 | |||||
11-12 | |||||
12-13 | |||||
13-14 | |||||
14-15 | |||||
15-16 | |||||
16-17 | |||||
17-18 | |||||
18-19 | |||||
19-20 | |||||
20-21 | |||||
21-22 |
Légendes:
Cours
Exercice, TP
Projet, labo, autre