Modul

oral examination of ca. 30 minutes

Students are able to

• understand basic structures and concepts from algebraic number theory,
• apply abstract concepts to concrete problems,
• read research papers and write a thesis in the field of algebraic number theory.

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• Algebraic number fields: rings of integers, Minkowski theory, class-groups and Dirichlet's unit theorem,
• Extensions of number fields: Ramified primes, Hilbert's ramification theory,
• Local fields: Ostrowski's theorem, valuation theory, Hensel's lemma, extensions of local fields,
• analytic methods: Dirichlet series, Dedekind's zeta function, L-series

The contents of the module "Algebra" are strongly recommended.

Total workload: 240 hours

Attendance: 90 h

• lectures, problem classes and examination

Self studies: 150 h

• follow-up and deepening of the course content,
• work on problem sheets,
• literature study and internet research on the course content,
• preparation for the module examination