Topics of the course
Dedekind domains; Minkowski theory; class number theorem; Dirichlet's unit theorem; valuations; completions; p-adic numbers; global and local fields; ramified, decomposed and inert primes; fundamental equality.
The course takes place from January 6 till February 27, every Tuesday, Thursday and Friday at 13:30--15:00 in room 228. The exercise classes take place on Tuesday, 10:00-12:00, in room 236 (Emilio Peixoto Assemany) and Thursdays, 10:00-12:00, in room 236 (Roberto Alvarenga Jr.).
There will be weekly exercises to solve, and an exam at the end of the course. While it is necessary to gain half of the amount of the achieveable points in the exercises to pass the course, only the results of the exam will determine the grade of the course.
The exam takes place on Thursday, February 26, 10:00--13:00 in room 228. The results will be presented the following day, February 27, at 13:00 in room 232.
Neukirch, J. - Algebraic Number Theory. Grundlehren der mathematischen Wissenschaften, Vol. 322, Springer-Verlag, 1999.
Lang, S. - Algebraic Number Theory. Graduate Texts in Mathematics, Vol. 110, Springer-Verlag, 1986.
Cassels, J.W.S., Froehlich, A. (editors) - Algebraic Number Theory. Proceedings of the instructional conference held at the University of Sussex, Brighton, September 1-17, 1965. Academic Press, Inc., London, 1986.
Weil, A. - Basic number theory. Die Grundlehren der mathematischen Wissenschaften, Vol. 144. Springer-Verlag New York, 1967.
An example of an extensions of rings of algebraic integers A and B such that B is not a free A-module can be found here.