Credits: 9

Type: advanced

Objectives:

Introduction to the basic tools used in algebraic number theory. The most important theorems in this field, including the Hermite, Minkowski, Dirichlet and Kronecker-Weber theorems.

Knowledge:

• Geometry of numbers.
• Diophantine equations.
• Local fields.
• Superior ramification.
• The Kronecker-Weber theorem.

Subject-specific competences:

• To use real networks to obtain the theorems of units, the finitude in the number of classes and in residues.
• To show understanding of finite extensions of p-adic number fields.
• To show understanding of the principles of Hilbert's theory of ramification.
• To be able to obtain the cyclotomic character of abelian extensions of rational number fields.