In this seminar, you'll learn how various concepts of the integers, for example the prime factorisation, can be generalised to finite field extensions of the rational numbers. For this manner, the more robust theory of Dedekind rings is worked out and combined with Galois theory.
Learning objective
- Understanding of Dedekind rings and factorisation of ideals as well as their class groups.
- Knowledge of how prime ideals may split under field extensions and how one may compute such a behaviour.
- Various insights into advanced algebraic, geometric, and analytic number theory, such as Kummer theory, Chebotarev's density theorem, Dirichlet's unit theorem, Dirichlet L-functions
Prerequisites / Notice
Algebra I & II, where the latter may also be visited in parallel.
Performance assessment
Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course