Derived Categories (Spring 2017)


Meeting time and place

Week 6 - 13 (6 Feb. -- 31 Mar.)
Time: Tuesday, 11:00 -- 13:00
Place: SP D1.160

Week 14 - 21 (3 Apr. -- 26 May)
Time: Tuesday, 13:00 -- 15:00
Place: SP G2.13

Exam

Time: 13:00 -- 16:00, Tuesday, 30 May
Place: Room G2.13

Schedule:
13:00 -- 13:25, Koen van Duin
13:30 -- 13:55, Joost van Dijk

It will be an oral exam. Final score is homework(40%) plus exam(60%).

Schedule

Lecture 1 (7 Feb): Examples of complexes
Lecture 2 (14 Feb): Abelian Categories 1
Lecture 3 (21 Feb): Abelian Categories 2, (Reference: [1], Section 5)
Lecture 4 (28 Feb): Derived Functors 1
Lecture 5 (7 Mar): Derived Functors 2
Lecture 6 (14 Mar): Hyper-derived Functors
Lecture 7 (21 Mar): Triangulated Categories, (Reference: [2], Section 3, 4)
Lecture 8 (28 Mar): The Homotopy Category 1, (Reference: [2], Section 8, 9, 10)
Lecture 9 (4 Apr): The Homotopy Category 2
Lecture 10 (11 Apr): Localisation of Categories
Lecture 11 (18 Apr): Derived Category as localisation
Lecture 12 (25 Apr): Derive Functors in Derived Categories
Lecture 13 (2 May): Derived Hom and Tensor
Lecture 14 (16 May): Derived Category of Coherent Sheaves I
Lecture 15 (23 May): Derived Category of Coherent Sheaves II. (Time 11:00 -- 13:00, Room C1.112)


Homework

Set 1, due date: Tuesday, 14 March.
Set 2, due date: Tuesday, 2 May.
Set 3, due date: Friday, 2 June.


References

[1]. Stacks Project: Chapter 12 (Homological Algebra).
[2]. Stacks Project: Chapter 13 (Derived Categories).
[3]. Sergei I. Gelfand and Yuri I. Manin, Methods of homological algebra.
[4]. Charles Weibel, An introduction to homological algebra.