2026/2027

Introduction to Algebraic Spaces and Stacks

Type: Optional course (faculty)

Delivered by: Faculty of Mathematics

Where: Faculty of Mathematics

When: 1, 2 module

Open to: students of one campus

Instructors: Alexander Pavlov

Language: English

ECTS credits: 6

Contact hours: 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.