Zahlentheorie 2 - Sommersemester 2017

Allgemeine Informationen

Ort (Vorlesungen): SR 119/A3 Seminarraum (Arnimallee 3-5)

Ort (Übungen): SR 009/A6 Seminarraum (Arnimallee 6)

Zeit: Dienstag 14:00-16:00, 16:00-18:00 (Vorlesungen) und Freitag 10:00-12:00 (Übungen)

Erster Termin: 18.04.2017

Unterrichtssprache: English

Beschreibung

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.

Klausur

Zeit: July 18 14:15-16:15

Ort: SR 119/A3 Seminarraum (Arnimallee 3-5)

Kommentar: You may bring two sheets of paper (DIN A4), each written by yourself and by hand with writing on both sides

Nachklausur

Zeit: Montag, 16. Oktober 2017, 10:00 - 12:00 Uhr

Ort: SR 032/A6 Seminarraum (Arnimallee 6)

Kommentar: You may bring two sheets of paper (DIN A4), each written by yourself and by hand with writing on both sides

Literatur

Die Vorlesung wird hauptsächlich folgenden Quellen folgen:

  • Milne, James: Algebraic Number Theory (available here)
  • Neukirch, Jürgen: Algebraische Zahlentheorie, Springer Verlag (English translation also available)

Nötige Vorkenntnisse

Linear Algebra I+II, Algebra and Number Theory I

Leitfaden

Here is a rough outline of the course (subject to changes):

1) Rings of integers

2) Basic properties of Dedekind domains

3) Minkowski's theory and finiteness of the class number

4) Dirichlet's Unit Theorem

5) Extensions of Dedekind domains and ramification theory

Übungen

  1. Übungablatt, April 18, 2017.
  2. Übungablatt, April 25, 2017.
  3. Übungablatt, May 2, 2017.
  4. Übungablatt, May 9, 2017.
  5. Übungablatt, May 17, 2017.
  6. Übungablatt, May 24, 2017.
  7. Übungablatt, May 31, 2017.
  8. Übungablatt, June 6, 2017.
  9. Übungablatt, June 13, 2017.
  10. Übungablatt, June 20, 2017.
  11. Übungablatt, July 4, 2017.
  12. Übungablatt, July 11, 2017.

Skript

Prüfung