Wintersemester 2009/2010 - Algebraic Number Theory

Link to the Moodle class room. (Password: "AlgNT")

If you intend to take this lecture, please register in the moodle class room. In case of any problems, please write me an e-mail.

Description of the lecture

In this lecture we will treat number fields and local fields. The main topics concerning number fields will be ideal arithmetic, the finiteness of the class group, Dirichlet's theorem on units and Hilbert's ramification theory. Concerning the second part, we will deal with metric fields, completions, Hensel's lemma, and Dedekind's and Hilbert's theorems on the different.

References

• See lecture.

Prerequisites

• Algebra.
• Interest in mathematics.

Exercise sheets

• Sheet 0 (for the first exercise class)
• Sheet 1 (to be handed in by 23 October 2009)
• Sheet 2 (to be handed in by 30 October 2009)
• Sheet 3 (to be handed in by 6 November 2009)
• Sheet 4 (to be handed in by 13 November 2009)
• Sheet 5 (to be handed in by 20 November 2009)
• Sheet 6 (to be handed in by 27 November 2009)
• Sheet 7 (to be handed in by 4 December 2009)
• Sheet 8 (to be handed in by 11 December 2009)
• Sheet 9 (to be handed in by 18 December 2009)
• Sheet 10 (to be handed in by 8 January 2010)
• Sheet 11 (to be handed in by 15 January 2010)
• Sheet 12 (to be handed in by 22 January 2010)
• Sheet 13 (to be handed in by 29 January 2010)

Last change: 22 January 2010