Group schemes are "groups" in the category of schemes, just as the usual groups are "groups" in the category of sets and Lie groups are "groups" in the category of smooth manifolds. An algebraic group is a group scheme whose underlying space is of finite type. In this course we are going to study algebraic groups in certain generality. Given a smooth algebraic group \(G\), we first split it into the connected part and the étale part using the connected-étale sequence. For a connected algebraic group we can split it further into an affine algerbaic group and an abelian variety using the theorem of Chevalley. Then we can find a maximal connected normal solvable subgroup of the affine algebraic group so that the quotient is semisimple. This normal subgroup is called the radical. There is also a maxiaml connected unipotent normal subgroup which is called the unipotent-radical. The aim of the course is to understand how can one decompose a smooth algebraic group in this way. We will introduce all the notions involved and prove most of theorems used.
The prerequests for this course is a first course in algebraic geometry.
If you want to get a grade, please contact me via email@example.com. There will be oral exams.
Every Tursday there will be a new exercise sheet. You can try to solve them, and if you have any questions please contact me at firstname.lastname@example.org.
Place (course): SR E.31/A7 (Arnimallee 7)
Place (exercise): SR 210/A3 Seminarraum (Arnimallee 3)
Date: Wednesday 10:00-12:00 and 14:00-16:00
First Appointment: 20.04.2016
Course Language: English