Algebraic Number Theory

A.Y. 2018/2019
Lesson for
9
Max ECTS
69
Overall hours
SSD
MAT/02
Language
Italian
Learning objectives
The course provides standard results in algebraic number theory, formulated both in the classical and in the adelic language.
Learning the basic results in Algebraic Number Theory with the ability of passing from the classical to the adelic language. Ability of computing the class groups and the group of units of a number field.

Course structure and Syllabus

Active edition
Yes
Responsible
Number Theory (first part)
MAT/02 - ALGEBRA - University credits: 6
Practicals: 20 hours
Lessons: 28 hours
Number Theory mod/2
MAT/02 - ALGEBRA - University credits: 3
Lessons: 21 hours
Number Theory (first part)
Syllabus
Part 1.
Dedekind domains (rings of integers), norms, traces and discriminants, the Theorem of Minkowski, finiteness of ideal classes, the Theorem of Hermite, the Theorem of Dirichlet.

Part 2.
Valuations, completions, quadratic forms over local and global fields. Classification and the Theorem of Hasse-Minkowski
Lesson period
Second semester
Lesson period
Second semester
Assessment methods
Esame
Assessment result
voto verbalizzato in trentesimi