Algebraic Number Theory

A.Y. 2017/2018
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.
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.
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, restricted products, review of Fourier theory, adele ring, idele group, classical results from the adelic perspecive, L-functions and functional equation.
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
Professor(s)
Reception:
On appointment
Via Cesare Saldini 50