Algebraic Number Theory Winter Term 17/18

 

News:

The first lecture will be on Wednesday, October 18

 

Dates: Monday, 12:00 (s.t) - 14:00 + Wednesday, 10:00 (p.m.) - 12:00; room: SR 6 (building 2.4)


Lecturer: Prof. Dr. Gabriela Weitze-Schmithüsen

contact: weitze [at] math.uni-sb.de
office hours: please contact me by email or just check whether I am here (room 301, E 2.4)
 

Teaching Assistant: Christian Steinhart

contact: steinhart [at] math.uni-sb.de
office hours: whenever I am here and wednesday 14-16 (room 302,  E 2.4)
 

Tutorials: Monday, 16:00 (c.t.) -  18:00 in SR9 (E 2.4, 3rd floor)

 

Topics:

Starting point in number theory is the study of solutions of equations over the integers possibly with several unknowns. This will lead us to the theory of number fields and their rings of integers.

In the lecture, we will cover in particular the following topics:

  • Rings of integers, Dedekind domains
  • Theory of ideals in Dedekind domains
  • Minkowski Theory
  • The Class Number and Dirichlet’s Unit Theorem 
  • Hilbert’s Ramification Theory
  • Cyclotomic Fields

Prerequisites:

The lecture "Einführung in Algebra und Zahlentheorie" and the lecture "Algebra" (preferably).


Literature:

 

  • S. I. Borevics, I. R. Safarevic: Zahlentheorie
  • H. Koch: Zahlentheorie
  • S. Lang: Algebraic Number Theory
  • J. Neukirch: Algebraische Zahlentheorie

 


Exercise Sheets:

Sheet
 sheet1
 sheet2
 sheet3
 sheet4
 sheet5
 sheet6
 sheet7
 sheet8