Stacks Notes

Here are my handwritten notes for the Fall 2022 course on Stacks, taught by David Zureick-Brown. Of course, these notes are not a loyal representation of the course. The target audience was my 2022 self. Keep in mind that all the errors are mine and the merits should be credited to the lecturer. Use at your own risk; I took this notes as a stacks novice and my inexperience surely shows.

  1. Why stacks?
  2. Categories
  3. Equivalence of Categories and (co)limits
  4. More (co)limits
  5. Even more (co)limits
  6. The functor of points
  7. The Yoneda embedding part II
  8. Grothendieck toplogies
  9. Sites and Topoi
  10. The canonical topology
  11. Functoriality
  12. Étaleness
  13. More adjectives
  14. Even more adjectives
  15. Flatness and algebraic spaces
  16. Algebraic spaces and equivalence realtions
  17. Equivalence relations and group actions
  18. Descent
  19. More descent
  20. 2-categories
  21. Fibered categories
  22. Stacks
  23. Algebraic stacks
  24. Stackification and quotient stacks

Author: Santiago Arango-Piñeros

Email: santiago.arango@emory.edu

Emacs 27.2 (Org mode 9.4.4)