2023/2024
Введение в коммутативную алгебру
Статус:
Дисциплина общефакультетского пула
Кто читает:
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
At its most basic level, algebraic geometry is the study of the geometry of solution sets of polynomial systems of equations. Classically, the coefficients of the polynomial equations are assumed to lie in an algebraically closed field. Considering more general coefficient rings, in particular rings of integers in number fields, one arrives at modern algebraic geometry and algebraic number theory. Commutative algebra provides the tools for answering basic questions about solutions sets of polynomial systems, such as finite gen- eration of the system, existence of solutions in some extension of the coefficient ring, dimension and irreducible components, and smoothness and singularities.