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)