Introduction to Derived Categories


Amnon Yekutieli, BGU


Abstract: We outline the construction of the derived category D(M) of an abelian category M. We then define left and right derived functors. We introduce K-projective, K-injective and K-flat resolutions, and prove existence of some derived functors when M is either the category of modules over a ring, or the category of sheaves of modules over a sheaf of rings. DG algebras and their derived categories will also be mentioned.

Next we discuss some more specialized topics: dualizing complexes (commutative and noncommutative), two-sided tilting complexes, derived Morita theory, and rigid dualizing complexes.


- Lecture notes are at http://www.math.bgu.ac.il/~amyekut/lectures/intro-der-cats/notes.pdf



(
May 2013)