2026/2027

Введение в алгебраическую теорию чисел

Статус: Дисциплина общефакультетского пула

Кто читает: Факультет математики

Где читается: Факультет математики

Когда читается: 3, 4 модуль

Охват аудитории: для всех кампусов НИУ ВШЭ

Преподаватели: Жгун Владимир Сергеевич

Язык: английский

Кредиты: 6

Контактные часы: 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.