2026/2027
Введение в алгебраические пространства и стеки
Статус:
Дисциплина общефакультетского пула
Кто читает:
Факультет математики
Где читается:
Факультет математики
Когда читается:
1, 2 модуль
Охват аудитории:
для своего кампуса
Преподаватели:
Павлов Александр Борисович
Язык:
английский
Кредиты:
6
Контактные часы:
60
Course Syllabus
Abstract
This course offers an introduction to the theory of algebraic spaces and stacks, a cornerstone of modern algebraic geometry. Born from the study of moduli spaces and the need to construct quotients by group actions, these concepts were formalized in the foundational work of Deligne, Mumford, and Artin.
The first part of the course that covers Grothendieck topologies, fibered categories, descent and stacks is based only on the category theory. But algebraic spaces/stacks requires working knowledge of algebraic geometry (e.g. Hartshorn’s textbook). One of the goals of the course is to include as many examples as time permits, in particular applications to constructions of various moduli spaces.