Algebraische Zahlentheorie

What it is about

You will learn the basic concepts and main theorems of algebraic number theory for number fields and their rings of integers. In the end you will be able to compute the norm, trace and discriminant, investigate the structure of ideals and the class group, and apply the theory to concrete examples such as quadratic and cyclotomic number fields.

What you will be able to do

• Understanding of number fields, norm and trace
• Determine algebraic rings of integers and integral basis
• Compute discriminants
• Apply ideal theory (Dedekind domains, prime factorization)
• Work with fractional ideals and the ideal class group
• Analyze special examples: quadratic and cyclotomic number fields
• (optional) Understanding of lattices and Dirichlet's unit theorem
• (optional) Understanding of the branching of prime ideals

What the module consists of

• VorlesungConveying the theoretical foundations and proofs
• ÜbungDiscussion of exercise sheets for deepening and applying the content

Teaching method

• Tafelvorlesungfor structured presentation of definitions and proofs
• Übungsblätterfor deepening and applying the methods in accompanying exercise sessions