Einführung in die Algebraische Zahlentheorie

What it is about

You will learn the foundations of algebraic number theory: number fields, rings of algebraic numbers and their ideal theory. In the end you can understand central concepts such as norm, trace, integrality, discriminant and units and apply the fundamental theorems to concrete problems and simple diophantine questions.

What you will be able to do

• Terms: number fields, algebraic integrality, norm and trace
• Compute integral bases and discriminants
• Understand ideal theory in Dedekind domains (prime factors, factor groups)
• Classify fractional ideals, class groups and class number
• Apply lattices and Dirichlet's unit theorem
• Apply the theory to quadratic and cyclotomic number fields

What the module consists of

• VorlesungTransmission of theoretical foundations and examples
• ÜbungDeepening and application of lecture content through exercises

Teaching method

• TafelvortragExplanation of theoretical principles and demonstration of examples
• ÜbungsaufgabenPractice and deepening of the lecture content