Universität Wien

250109 VO Algebraic Groups (2025W)

6.00 ECTS (4.00 SWS), SPL 25 - Mathematik
Moodle

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Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

The lecture course starts on Monday, 6th of October 2025

  • Wednesday 01.10. 11:30 - 13:00 Seminarraum 4 Oskar-Morgenstern-Platz 1 1.Stock
  • Monday 06.10. 15:00 - 16:30 Seminarraum 5 Oskar-Morgenstern-Platz 1 1.Stock
  • Wednesday 08.10. 11:30 - 13:00 Seminarraum 4 Oskar-Morgenstern-Platz 1 1.Stock
  • Monday 13.10. 15:00 - 16:30 Seminarraum 5 Oskar-Morgenstern-Platz 1 1.Stock
  • Wednesday 15.10. 11:30 - 13:00 Seminarraum 4 Oskar-Morgenstern-Platz 1 1.Stock
  • Monday 20.10. 15:00 - 16:30 Seminarraum 5 Oskar-Morgenstern-Platz 1 1.Stock
  • Wednesday 22.10. 11:30 - 13:00 Seminarraum 4 Oskar-Morgenstern-Platz 1 1.Stock
  • Monday 27.10. 15:00 - 16:30 Seminarraum 5 Oskar-Morgenstern-Platz 1 1.Stock
  • Wednesday 29.10. 11:30 - 13:00 Seminarraum 4 Oskar-Morgenstern-Platz 1 1.Stock
  • Monday 03.11. 15:00 - 16:30 Seminarraum 5 Oskar-Morgenstern-Platz 1 1.Stock
  • Wednesday 05.11. 11:30 - 13:00 Seminarraum 4 Oskar-Morgenstern-Platz 1 1.Stock
  • Monday 10.11. 15:00 - 16:30 Seminarraum 5 Oskar-Morgenstern-Platz 1 1.Stock
  • Wednesday 12.11. 11:30 - 13:00 Seminarraum 4 Oskar-Morgenstern-Platz 1 1.Stock
  • Monday 17.11. 15:00 - 16:30 Seminarraum 5 Oskar-Morgenstern-Platz 1 1.Stock
  • Wednesday 19.11. 11:30 - 13:00 Seminarraum 4 Oskar-Morgenstern-Platz 1 1.Stock
  • Monday 24.11. 15:00 - 16:30 Seminarraum 5 Oskar-Morgenstern-Platz 1 1.Stock
  • Wednesday 26.11. 11:30 - 13:00 Seminarraum 4 Oskar-Morgenstern-Platz 1 1.Stock
  • Monday 01.12. 15:00 - 16:30 Seminarraum 5 Oskar-Morgenstern-Platz 1 1.Stock
  • Wednesday 03.12. 11:30 - 13:00 Seminarraum 4 Oskar-Morgenstern-Platz 1 1.Stock
  • Wednesday 10.12. 11:30 - 13:00 Seminarraum 4 Oskar-Morgenstern-Platz 1 1.Stock
  • Monday 15.12. 15:00 - 16:30 Seminarraum 5 Oskar-Morgenstern-Platz 1 1.Stock
  • Wednesday 17.12. 11:30 - 13:00 Seminarraum 4 Oskar-Morgenstern-Platz 1 1.Stock
  • Wednesday 07.01. 11:30 - 13:00 Seminarraum 4 Oskar-Morgenstern-Platz 1 1.Stock
  • Monday 12.01. 15:00 - 16:30 Seminarraum 5 Oskar-Morgenstern-Platz 1 1.Stock
  • Wednesday 14.01. 11:30 - 13:00 Seminarraum 4 Oskar-Morgenstern-Platz 1 1.Stock
  • Monday 19.01. 15:00 - 16:30 Seminarraum 5 Oskar-Morgenstern-Platz 1 1.Stock
  • Wednesday 21.01. 11:30 - 13:00 Seminarraum 4 Oskar-Morgenstern-Platz 1 1.Stock
  • Monday 26.01. 15:00 - 16:30 Seminarraum 5 Oskar-Morgenstern-Platz 1 1.Stock
  • Wednesday 28.01. 11:30 - 13:00 Seminarraum 4 Oskar-Morgenstern-Platz 1 1.Stock

Information

Aims, contents and method of the course

The theory of algebraic groups emerged from the wish to create an analog of the theory of Lie groups or analytic matrix groups like GL(n,R), R the real numbers, for algebraic matrix groups like GL(n,K), where K is any abstract (algebraically closed) field. To this end analytic notions and concepts or arguments were replaced by purely algebraic constructions, starting with the notion of an algebraic groups which is an analog of the notion of a Lie group. The result was a closed theory, to a large extent analogous to the theory of Lie groups, which proved very succesful in all contexts and applications where algebraic groups appeared (number theory, (algebraic) geometry, representation theory, ...).

In the lecture course we want to give an introduction to the foundations and basic notions of the theory of affine (or linear) algebraic groups.

Prerequisites/helpful are a knowledge of basic notions of algebraic geometry ("affine varieties").

Assessment and permitted materials

Oral exam

Minimum requirements and assessment criteria

To pass the oral exam

Examination topics

Content of the lecture course

Reading list

The classical references for the theory of linear algebraic groups are

A. Borel "Linear Algebraic groups"

J. Humphreys "Linear Algebraic groups"

T. Springer "Linear Algebraic groups"

For connections with number theory:

V. Platonov, A. Rapinchuk "Algebraic groups and number theory"

Association in the course directory

MALV; ML2; MEL

Last modified: Mo 04.05.2026 10:07