Introduction to Algebraic Number Theory

Lecturer: Prof. Dr. Özlem Imamoglu

Coordinator: Dr. Danylo Radchenko

Room: HG D 1.1

Time: Tue, 9.15 - 10.00 and Thu, 10.15 - 11.55

The first class will take place on Thursday September 19.

Content

• Algebraic integers
• The ideal class group
• Geometry of numbers
• Finiteness of the ideal class group
• Dirichlet's unit theorem
• Ramification theory
• \(\zeta\)-functions of number fields and the class number formula

... and more, if time permits.

Prerequisites

Students should be familiar with Algebra as taught in the mandatory second-year course at ETH Zurich (particularly, Galois-theory).

Exercises

Tutor: Alessandro Lägeler

Exercise classes will take place on Mondays in ML J 34.3 at 15.15-16.00 and on Tuesdays in HG G 26.1 at 14.15-15.00. The new exercises will be available every Friday.

You may hand in your solutions either in class or in the assistant's box at HG J 68.

Literature

Some suggestions for literature may be found here.

• Lectures in Algebraic Number Theory by E. Hecke (Springer, 1981) 
• Number Fields by D. Marcus (Springer, 2018) 
• Algebraic Theory of Numbers by P. Samuel (Dover, 2008) 
• Algebraic Number Theory by J. Neukirch (Springer 1999), also available in German 

More advanced texts

• Algebraic Number Theory by J.W.S. Cassels and A. Fröhlich (Inc., Washington, DC, 1967) 
• Algebraic Number Theory by S. Lang (Springer 1994)