The discussion of the previous chapter is applied to the derived category of the abelian category of coherent sheaves. The Serre functor is introduced, and particular spanning classes are constructed. The usual geometric functors, direct and inverse image, tensor product, and global sections, are derived and extended to functors between derived categories. The compatibilities between them are reviewed. The final section focuses on the Grothendieck-Verdier duality.
Keywords: coherent sheaf, higher direct image, derived tensor product, Grothendieck-Verdier duality