250414 VO Selected topics in Number Theory (2006S)

he main focus of these lectures will be the theory of Chevalley groups. In particular, this refers to the construction of the group scheme over the integers for the adjoint group of a given type g ( g a complex semisimple Lie algebra). We will discuss various applications of this fundamental approach relating Lie theory and the (arithmetic) theory of algebraic groups. The course presupposes the theory of complex semisimple Lie algebras through the classification, as may be found, for example, in the book J.E. Humphreys, Introduction to Lie Algebras and Representation theory, Springer-Verlag, Berlin-Heidelberg New York.