In this second talk, the topic of derived categories will be discussed: the main focus will be the
derived category of coherent sheaves of a smooth projective variety, and its triangulated structure.
Here we will follow Chapters 2 and 3 of
Huybrechts' book
as a main source.
Construction of the derived category of an abelian category: category of (bounded) complexes and its shift functor, quasi-isomorphisms,
homotopy category, cones, localization.
The category of (quasi-) coherent sheaves of a smooth projective variety. The derived category of coherent sheaves
and its triangulated structure.
Derived functors, derived homs, pullbacks and pushforwards, cohomology objects.