Deligne-Lusztig theory - Sommersemster 2019

Dr. Alexander Ivanov
Endenicher Allee 60 · Zimmer 1.004
Tel.: 0228-73-3791
E-mail: ivanov (ergänze

Time and Place

Tuesday, 8-10h, Seminarraum 0.008
First Lecture: Tuesday 9.4.2029.
Please note: there will be no lecture on Tuesday, April 2nd!


The basic knowledge of group theory and algebraic geometry is required. It is also essential to understand (at least the basic notions of) algebraic groups.

Content of the course

This course will cover the Deligne-Lusztig theory. We will construct certain varieties - called Deligne-Lusztig varieties - over finite fields, attached to reductive groups. The main reason to study these varieties is that their etale cohomology encodes all irreducible representations (with coefficients in an algebraically closed field of characteristic zero) of finite reductive groups.


  • Deligne, P. and Lusztig, G.: "Representations of reductive groups over finite fields", Ann. of Math., 103(1): 103-161, 1976.
  • Carter, R.: "Finite groups of Lie-type", Wiley 1985
  • Digne, F. and Michel J.: "Representations of finite groups of Lie-type", Camb. Univ. Press, 2014
  • Cabanes, M. and Enguehard, M.: "Representation theory of finite reductive groups", Camb. Univ. Press, 2014.

Exercise sessions

There will be no exercise sessions for this lecture.

Last modified: 30.03.2019, Alexander Ivanov