A modern introduction to algebraic stacks

Time and place

Room 509, Cosmology Bldg., National Taiwan University
Mondays 16:00 – 17:30, 10/31/22 – 1/16/23
Links for online attendance available at the official course page.


In these lectures we will give a modern introduction to the theory of algebraic stacks, using the language of ∞-categories (which will be reviewed in the first few lectures). The value of this machinery will be illustrated through our discussion of topics like the cotangent complex, and the theories of coherent sheaves and perfect complexes on stacks. These abstract concepts will be illustrated through various examples such as moduli stacks of curves, vector bundles and coherent sheaves. We will assume the audience has some basic background in algebraic geometry (scheme theory) and algebraic topology.

Lecture notes

Notes (last lecture finally added 10/2/23) (updated notes)

Official course page