Kirill Zainoulline: Algebraic Geometry

11th January, 2021

This is a 23-lecture course, with each lecture being around 80 minutes, given online by Kirill Zainoulline. It gives an introduction to algebraic geometry.

A brief overview of commutative algebra: rings and ideals, Nakayama’s Lemma, localization, Krull-dimension, direct-limits, integral dependence. Toward algebraic varieties: Regular functions, algebraic sets, Hilbert’s Nullstellensatz, Zariski topology, ringed spaces, affine and projective varieties. Toward sheaves and group schemes: functors of points, Grothendieck topologies, representable functors, group schemes, tori, Grassmannians, torsors and twisted forms, quadrics and Severi-Brauer varieties.

  1. Lecture 1
  2. Lecture 2
  3. Lecture 3
  4. Lecture 4
  5. Lecture 5
  6. Lecture 6
  7. Lecture 7
  8. Lecture 8
  9. Lecture 9
  10. Lecture 10
  11. Lecture 11
  12. Lecture 12
  13. Lecture 13
  14. Lecture 14
  15. Lecture 15
  16. Lecture 16
  17. Lecture 17
  18. Lecture 18
  19. Lecture 19
  20. Lecture 20
  21. Lecture 21
  22. Lecture 22
  23. Lecture 23

These videos were produced by the Fields Institute, as a Fields Academy course.