This course gives an introduction to algebraic number theory. The main objects of study are number fields, i.e. finite extensions of the field of rational numbers. To a number field K we will attach its ring of integers. This ring is a Dedekind domain and we will see that one of its invariants is the class number, which measures "how far" the ring is away from being a unique factorization domain. We will also study finite extensions of number fields, and how the prime ideals behave in the associated extensions of the rings of integers.
Here is a rough outline of the course (subject to change):
1) Rings of integers
2) Basic properties of Dedekind domains
3) Minkowski's theory and finiteness of the class number
4) Dirichlet's Unit Theorem
5) Extensions of Dedekind domains and ramification theory
Nähere Angaben zum Programm der Vorlesung finden Sie hier: