Algebraic Number Theory (summer 2017)


The course takes place from January 3 till February 24, every Tuesday, Thursday and Friday at 13:00--15:00 in room 349. The course is accompanied by an weekly exercise class on Monday at 15:00--17:00 in room 349, which is supervised by Valdir Jose Pereira Junior.

The grade of the course will be determined by a final exam at the end of the course. The exam takes place on Tuesday, February 21, at 13:00--16:00 in room 349.

There will be weekly exercise lists, which are not mandatory but strongly recommended to hand in. A good score for the exercises can substitute 10% of the exam's score and therefore improve the final grade of the course.

Changes in the schedule

The class on Thursday, February 9, will begin delayed at 14:00.

Exercise lists

List 1

List 2

List 3

List 4

List 5

List 6

List 7


J. Neukirch - Algebraic Number Theory. Grundlehren der mathematischen Wissenschaften, Vol. 322, Springer-Verlag, 1999.

O. Endler - Teoria dos Números Algébricos. Rio de Janeiro, IMPA, Projeto Euclides, 1986.

S. Lang - Algebraic Number Theory. Graduate Texts in Mathematics, Vol. 110, Springer-Verlag, 1986.

J. S. Milne - Algebraic Number Theory, available at

Further readings

An example by Keith Conrad of an extensions of rings of algebraic integers A and B such that B is not a free A-module:

A text by Hendrik Lenstra on the Pell equation:

Franz Lemmermeyer's list of proofs of the quadratic reciprocity law:

An example by Brian Conrad of a Galois extension with inseparable residue field extension: see section 2 of

Carl Erickson's notes on cyclotomic fields and proofs of Fermat's last theorem for some exponents:

A handout by Brian Conrad showing that every finite extension of a local field can be realized as a completion of a global field: see section 2 of

A text by Sungjin Kim about the Hasse-Minkowski theorem: