Derived Algebraic Geometry

General information

Instructor Shane Kelly
Email shanekelly [at] g.ecc [dot] u-tokyo [dot] ac.jp
Webpage https://www.ms.u-tokyo.ac.jp/~kelly/Course2025DAG/2025DAG.html
Main References [HTT] Lurie, "Higher Topos Theory" pdf
[DAG] Lurie, "Derived algebraic geometry" pdf
[Toën] Toën, "Derived algebraic geometry" pdf
Other References [SAG] Lurie, "Spectral algebraic geomegry" pdf
[HA] Lurie, "Higher Algebra" pdf
Room Graduate School of Mathmatical Science Bldg. , Room 118.
Time Wed(水) 10:25-12:10
Assessment Exercises will be given during the lectures. To pass the course, it is enough to submit solutions to at least one exercise from each of the first 10 lectures (so at least 10 exercises, but you are welcome to submit as many solutions as you want).

Outline

1. Introduction (4月9日)

2025DAG01.pdf

We use Bezout's Theorem to argue that moving from sets to homotopy types is a natural progression, analogous to fields ⇝ algebraically closed fields; affine varieties ⇝ projective varieties; varities ⇝ schemes.

--- 4月16日 No lecture 講義がありません ---

(April 14-18 Workshop Arithmetic France-Japan - 日本 x フランス 数論幾何学 2025)

2. Homotopy types (4月23日)

2025DAG02.pdf

We present two models for the theory of homotopy types: simplicial sets (or rather Kan complexes) and topological spaces (or rather CW complexes). Most importantly, we define what is a space and a equivalence.

--- 4月30日 No lecture 講義がありません ---

3. (5月7日)

4. (5月14日)

5. (5月21日)

6. (5月28日)

7. (6月4日)

8. (6月11日)

9. (6月18日)

10. (6月25日)

--- 7月2日 No lecture 講義がありません ---

--- 7月9日 No lecture 講義がありません ---

11. (7月16日)