Department Mathematik
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Algebraic Groups


Summersemester 2018


Seminar description

Time and place: Wednesdays, 16-18 in Room B045.

Main reference: new book of Milne "Algebraic groups" (2017).

Information: The seminar will be conducted in English. The first meeting will be on Wednesday, 11th of April. The seminar is intended for Master students (prerequisites: algebra, commutative algebra and algebraic geometry).
Please write me an email if you want to attend the seminar and give a talk.

Preliminary programm:


1. Introduction. Distribution of the talks. 11th of April.

2. Topological groups and Pontryagin duality (Andrei Lavrenov). 18th of April.

3. Hopf algebras, comodules, properties, examples (Max Zeuner). 25th of April. References: Milne, from Chapters 1-4.

4. Affine algebraic groups, linear representations, affine algebraic groups are linear (Kilian Rückschloß). 2nd of May. References: Milne, from Chapters 1-4.

5. Recovering a group from its representations (Andrei Lavrenov). 9th of May. References: Milne, Chapter 9.a

6. Jordan decomposition (Maksim Zhykhovich). 16th of May. References: Milne, Chapter 9.b

7. Tannakian duality (Kilian Rückschloß). 23rd of May. References: Milne, Chapter 9.c-f

8. The Lie algebra of an algebraic group (Max Zeuner). 30th of May. References: Milne, Chapter 10b,d,e

9. Groups of multiplicative type I (Maksim Zhykhovich). 6th of June. References: Milne, from Chapter 12a-e

10. Groups of multiplicative type II (Maksim Zhykhovich). 13th of June. References: Milne, from Chapter 12f-m

11. Borel subgroups I (Andrei Lavrenov). 20th of June. References: Milne, Chapter 17.

12. Applications of the Morava K-theory to algebraic groups and quadrics (Nikita Semenov) in the Seminar "Arithmetische und Algebraische Geometrie" 16:00-17:00 (Room 251), 27th of June.

13. Borel subgroups II (Andrei Lavrenov). 4th of July. References: Milne, Chapter 17.

14. Root datum (Kilian Rückschloß), 11th of July.