401-2140-21L Seminar in Algebraic Number Theory
|Spring Semester 2021
|Language of instruction
|Number of participants limited to 12.
|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.
|- 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.