Algebraic Number Theory

What it is about

You deal with number fields (finite extensions of Q) and their rings of integers. You learn central concepts such as integral dependence, Dedekind domains, ideal class groups, ramification and étale algebras as well as classical analytical results such as the Hermite–Minkowski theorem and Dirichlet’s theorems on class groups and unit groups. In the end you will be able to apply the main theorems and solve problems on number fields, integers and simple diophantine equations.

What you will be able to do

• Understanding of number fields and rings of integers
• Knowledge of integral dependence and Dedekind domains
• Understanding and applying the concept of the ideal class group
• Understanding ramification in extensions and étale algebras
• Applying analytical results: Hermite–Minkowski and Dirichlet theorems
• Solving concrete problems on number fields and diophantine examples

What the module consists of

• VorlesungConveying the theoretical foundations
• Übung/Practice sessionDiscussion and deepening of the exercise sheets

Teaching method

• TafelvorlesungIntroduction and derivation of the theory
• Übungsblätter mit ÜbungssitzungenDeepening and application of the learned material through exercises