2026/2027
Introduction to Derived Algebraic Geometry
ID 1250043
Type:
Optional course (faculty)
Delivered by:
Faculty of Mathematics
Where:
Faculty of Mathematics
When:
3, 4 module
Open to:
students of one campus
Instructors:
Alexander Pavlov
Language:
English
ECTS credits:
6
Contact hours:
72
Course Syllabus
Abstract
"Derived algebraic geometry is an extension of algebraic geometry that provide a setting to treat geometrically bad situations (bad intersections, quotients by bad actions etc). It is a natural generalization of the theory of stacks used in algebraic in the context of higher algebra.
The course is introductory, but it assumes familiarity with stacks and infinity-categories (quasi-categories). The results from these areas will be reviewed, but many proofs will be sketched or omitted. We will focus on the basic language of derived algebraic geometry: derived stacks and quasi-coherent sheaves on them. If time permits, we will cover the category of ind-coherent sheaves. The category of Ind-coherent sheaves is analogous to the (derived and enhanced) category of quasi-coherent sheaves, but has nicer properties in some respects."