References:

[1] Keune F. - Number Fields
[2] Neukirch J. - Algebraic Number theory
[3] Fesenko I. - Core Topics in Number Theory I

Schedule:
Every Thursday 13:30 - 15:55, 
Room E13-207
 

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Classroom diary (September-December 2026):

1 - 03/09 - Number fields and lattices. Integrality. Norm and trace of a finite extension.

2 - 10/09 - More on norm and trace. The discriminant of a base in a field extension. Ring of integers seen as euclidean lattices.

3 - 17/09 - The discriminant of a number field. Stickelberger theorem. Dedekind domains and their properties.

4 - 24/09 - More on Dedekind domains: unique factorization of ideals. Ideal valuation. Chinese remainder theorem. Any ideal is generated by two elements.

5 - 08/10 - Ideal class group. Fractional ideals. Ideal class group as quotient group. Fundamental exact sequence for the group of fractional ideals.
6 - 15/10 - Characterization of Dedekind domains. O_K is a Dedekind domain. Factorization of prime numbers in O_K. Ramification, inertia and dimensional formula.

7 - 22/10 - Dedekind-Kummer theorem. Factorization of ideals in Galois extensions. Norm of ideals. Multiplicativity of the norm and applications