Teoria dei Numeri (laurea magistrale in Matematica) - anno 2011-12

riferimenti bibligrafici:
- Janusz, Gerald J. Algebraic number fields. Second edition. Graduate Studies in Mathematics, 7. American Mathematical Society, Providence, RI, 1996. x+276 pp.
- Algebraic number theory. Proceedings of the instructional conference held at the University of Sussex, Brighton, September 1--17, 1965. Edited by J. W. S. Cassels and A. Fröhlich. Reprint of the 1967 original. Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London, 1986. xviii+366 pp.

Programma del corso
Anelli di valutazione discreta. Domini di Dedekind. Estensioni di domini di Dedekind.
Il teorema delle unità di Dirichlet. Finitezza del numero di classi di ideali.
Valutazioni e completamenti.

Parte avanzata:
Serie di Dirichlet. Funzioni L.
Introduzione alla teoria dei corpi di classe.



Number theory (Algant curriculum) - year 2011-12

references:
- Janusz, Gerald J. Algebraic number fields. Second edition. Graduate Studies in Mathematics, 7. American Mathematical Society, Providence, RI, 1996. x+276 pp.
- Algebraic number theory. Proceedings of the instructional conference held at the University of Sussex, Brighton, September 1--17, 1965. Edited by J. W. S. Cassels and A. Fröhlich. Reprint of the 1967 original. Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London, 1986. xviii+366 pp.

Program
Discrete valuation rings. Dedekind domains. Extensions of Dedekind domains.
Dirichlet's unit theorem. Finiteness of the class group.
Valuations and completions.

Advanced part:
Dirichlet series. L-functions.
Introduction to class field theory.



Exams 2010-11
Exam 26-1-11
Exam 17-2-11

Exams 2011-12
Exam 1-2-12
Exam 15-2-12