Summer Graduate School

The goal of the school is to give an introduction to basic techniques for working with derived categories, with an emphasis on the derived categories of coherent sheaves on algebraic varieties. A particular goal will be to understand Orlov’s equivalence relating the derived category of a projective hypersurface with matrix factorizations of the corresponding polynomial.

Suggested prerequisites:

The students will be assumed to be familiar with basic algebraic geometry, including the notion of a coherent sheaf on an algebraic variety (covered in Sec. 1–5 of ch.2 of Hartshorne’s “Algebraic Geometry”), and basic derived functors and sheaf cohomology (see Sec. 1,2 and 4 of ch.3 of the same book). 

Bibliography (PDF)

Exercises
Exercise 1
Exercise 2
Exercise 3
Exercise 4
Exercise 5
Exc-coll Exercise
Exc-coll Exercise 2