Zahlentheorie II
Alexandru Constantinescu
Zusätzl. Angaben / Voraussetzungen
Voraussetzungen:
Algebra I
Kommentar
This course gives an introduction to algebraic number theory. The main objects of study are number fields, i.e. finite extensions of the field of rational numbers. To a number field K we will attach its ring of integers. This ring is a Dedekind domain and we will see that one of its invariants is the class number, which measures "how far" the ring is away from being a unique factorization domain. We will also study finite extensions of number fields, and how the prime ideals behave in the associated extensions of the rings of integers.
Here is a rough outline of the course (subject to change):
1) Diophantic equations
2) Rings of integers
3) Basic properties of Dedekind domains
4) Minkowski's theory and finiteness of the class number
5) p-adic numbers
Voraussetzungen:
Algebra I und Algebra&Zahlentheorie
SchließenLiteraturhinweise
- James Milne: Algebraic Number Theory (frei verfügbar hier )
- Jürgen Neukirch: Algebraische Zahlentheorie, Springer Verlag (English translation also available)
- Alexander Schmidt: Einführung in die Algebraische Zahlentheorie
26 Termine
Zusätzliche Termine
Mo, 22.07.2024 10:00 - 13:00Regelmäßige Termine der Lehrveranstaltung