Algebraic Number Theory
A.Y. 2018/2019
Learning objectives
The course provides standard results in algebraic number theory, formulated both in the classical and in the adelic language.
Expected learning outcomes
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.
Lesson period: Second semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Responsible
Lesson period
Second semester
Number Theory (first part)
Course 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
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
Number Theory (first part)
MAT/02 - ALGEBRA - University credits: 6
Practicals: 20 hours
Lessons: 28 hours
Lessons: 28 hours
Professors:
Andreatta Fabrizio, Seveso Marco Adamo
Number Theory mod/2
MAT/02 - ALGEBRA - University credits: 3
Lessons: 21 hours
Professors:
Andreatta Fabrizio, Seveso Marco Adamo
Professor(s)