Programme | |
Topic 1: | Discrete valuation rings. Dedekind domains. Extensions of Dedekind domains. |
Topic 2: | Dirichlet's unit theorem. Finiteness of the class group. |
Topic 3: | Valuations and completions. |
Part 2: | Dirichlet series. L-functions. Introduction to class field theory (to be confirmed). |
Note: | Every suggestion from the students will be welcome, in particular it will be possible to (partially) modify the second part of the program according to their needs and interest. |
Bibliography | |
G. J. Janusz: Algebraic number fields, Second edition. Graduate Studies in Mathematics, 7. American Mathematical Society, Providence, RI, 1996. | |
J. W. S. Cassels and A. Fröhlich (editors): Algebraic number theory, Proceedings of the instructional conference held at the University of Sussex, Brighton, September 1--17, 1965. Reprint of the 1967 original. Academic Press, Inc., London, 1986. |
Tuesday | 12.30-14.30 | Room 8 |
Wednesday | 8.30-10.30 | Room 3 |
Friday | 8.30-10.30 | Room 3 |
In order to be elegible for the exam for the first part, you have to produce in written form the solutions of some exercises which will be posted here below. Then, a written exam (3/4 problems, 2 hours) + oral discussion. For the advanced part, you have also to prepare a one-hour seminar discussing an argument which has to be communicated to (and approved by) me in written form (LaTeX/PDF) at least two weeks in advance.
Week 1 | Week 2 | Week 3 | Week 4 | Week 5 | Week 6 |
Seminar: Monday, February 24, 15.30--16.30, Room 7 |
Speaker: Alexey Beshenov |
Institution: Univ. Bourdeaux |
Title: K-gruppi e campi numerici. |
Abstract: Spiegherò cosa sono i K-gruppi algebrici di un anello e come essi siano collegati all'aritmetica dei campi numerici. Introdurrò alcuni risultati classici e le congetture ancora non risolte. |