Derived functors have powerful applications in algebraic geometry, in particular for formulating dualities, and for working with cohomology in relative settings. This course will develop their theory, along with ways to calculate them. I will introduce the derived category, which gives a natural setting for derived functors, and some basic birational geometry, which gives a supply of interesting examples. Towards the end, I will explain topics of current research interest in this area, such as categorified perverse sheaves and noncommutative resolutions.

Basic algebraic geometry, and introductory homological algebra, will be helpful.

D. Huybrechts, Fourier-Mukai transforms in algebraic geometry, Oxford, Math