401-2140-21L  Seminar in Algebraic Number Theory

SemesterSpring Semester 2021
LecturersR. Steiner
Periodicitynon-recurring course
Language of instructionGerman
CommentNumber of participants limited to 12.

AbstractIn 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.
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 / NoticeAlgebra I & II, where the latter may also be visited in parallel.