Coursebooks

Linear algebraic groups

MATH-479

Lecturer(s) :

Urech Christian Lucius

Language:

English

Summary

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

Content

first definitions and properties, morphisms, dimension, Jordan decomposition, tangent space

commutative connected groups, tori, connected solvable groups,

Lie algebra

group actions on algebraic varieties and some invariant theory

Keywords

algebraic groups

group actions on algebraic varieties

Lie algebra

algebraic geometry

group theory

Learning Prerequisites

Required courses

at least one introductory algebraic geometry course, group theory

Recommended courses

Background in group theory, Lie theory and some algebraic geometry

Learning Outcomes

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

Teaching methods

Lectures and exercises

Expected student activities

exercises and presentations

Assessment methods

Part of the grade will be based upon student presentation of some course material during the exercise sessions or corrected written homework assignments, or both.

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

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

In the programs

  • Mathematics - master program, 2020-2021, Master semester 2
    • Semester
      Spring
    • Exam form
      Oral
    • Credits
      5
    • Subject examined
      Linear algebraic groups
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks
  • Applied Mathematics, 2020-2021, Master semester 2
    • Semester
      Spring
    • Exam form
      Oral
    • Credits
      5
    • Subject examined
      Linear algebraic groups
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks
  • Applied Mathematics, 2020-2021, Master semester 4
    • Semester
      Spring
    • Exam form
      Oral
    • Credits
      5
    • Subject examined
      Linear algebraic groups
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks

Reference week

MoTuWeThFr
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
Under construction
Lecture
Exercise, TP
Project, other

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  • Autumn semester
  • Winter sessions
  • Spring semester
  • Summer sessions
  • Lecture in French
  • Lecture in English
  • Lecture in German