2026/2027

Introduction to Algebraic Number Theory

Type: Optional course (faculty)

Delivered by: Faculty of Mathematics

Where: Faculty of Mathematics

When: 3, 4 module

Open to: students of all HSE University campuses

Instructors: Vladimir Zhgoon

Language: English

ECTS credits: 6

Contact hours: 72

Course Syllabus

Abstract

Algebraic number theory is a classical field of mathematics that was formed during the study of solutions to Diophantine equations, as well as through attempts to prove Fermat's theorem. Now it is a vast classical field underlying Arithmetic geometry. In this course, we will recall the basics of Galois theory, consider the so-called branching theory, prove the main theorems on the structure of ideals (decompositions into simple ideals), prove Dirichlet's theorem on the structure of S-units and the finiteness theorem of a class group. We will highlight a very important analogy between the theory of algebraic numbers and the theory of algebraic curves over finite fields.