250066 VO Algebraic groups (2017S)

The theory of algebraic groups has emerged from a synthesis of the study of Lie groups on the one hand and of matrix groups like GL(n,K) or O(n,K) over arbitrary fields K on the other hand. Thus, algebraic groups are purely algebraic analogues of Lie groups. Nowadays algebraic groups have acquired a central position in number theory and (algebraic) geometry. Their theory has many contact points to arithmetic, geometry, representation theory and basic knowledge of algebraic groups is a prerequisite for understanding many results in number theory and geometry. In the course we want to give an introduction to the foundations of the theory of algebraic groups.

Prerequisites are: Possibly knowledge of basic notions of algebraic geometry; knowledge of basics of Lie groups is helpful though not necessary.

In the first lecture there will be a preliminary discussion.