Number Theory

dott. G. Molteni

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.

Lectures

Tuesday 12.30-14.30 Room 8
Wednesday 8.30-10.30 Room 3
Friday 8.30-10.30 Room 3




Exam

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.


Homework for the current A.Y.

Week 1 Week 2 Week 3 Week 4 Week 5 Week 6

Homeworks for the passed years: sheet 1, sheet 2.

Some exercises


News

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.

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Responsabile del sito: Giuseppe Molteni
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