All Questions

I am reading the dualizing sheaf and duality theorems from Hartshorne’s algebraic geometry book. I am wondering about the following. When does the dualizing sheaf of a projective scheme is an locally ...

$\DeclareMathOperator{\Spec}{Spec} \DeclareMathOperator{\hom}{\mathcal{Hom}} \DeclareMathOperator{\ox}{\mathcal{O}_X}$Let $f:X \to Y$ be a proper morphism. In section 6.4. of Liu's book he introduces ...