Algebraic Number Theory 2

What it is about

You will learn p-adic numbers Q_p and their finite field extensions (local fields) and their parallels to global algebraic number theory. A focus is the local class field theory, which relates abelian finite Galois extensions of a local field to suitable subgroups of the field. In the end you can apply properties of extensions of local fields (ramified, unramified, tam) and use simple statements of local class field theory.

What you will be able to do

• Understanding of p-adic numbers and local fields
• Knowledge of discrete valuations and ramification concepts
• Application of group cohomology in local contexts
• Familiarity with the main theorems of local class field theory
• Applying the learned theorems to concrete examples and problems

What the module consists of

• VorlesungConveying the theory on local fields, ramification and class field theory
• Übung/ÜbungssitzungenDiscussion of problem sheets for deepening and practice

Teaching method

• TafelvorlesungExplaining the theory and deriving results
• Übungsblätter mit SessionsDeepening and application of concepts in examples