This question refers to the proof of Proposition 2.3/IV in Hartshorne, page 301. Let $R$ be the ramification divisor associated to a finite, separable morphism of curves $f:X \rightarrow Y$. Why is it true that $\Omega_{X/Y} \otimes \Omega_{X}^{-1} = O_R$?
Edited: More specifically the proof starts by tensoring the sequence $0 \rightarrow f^* \Omega_Y \rightarrow \Omega_X \rightarrow \Omega_{X/Y} \rightarrow 0$ with $\Omega_X^{-1}$ and getting $0 \rightarrow f^* \Omega_Y \otimes \Omega_X^{-1} \rightarrow O_X \rightarrow \Omega_{X/Y} \otimes \Omega_X^{-1} \rightarrow 0$. But instead of $\Omega_{X/Y} \otimes \Omega_X^{-1}$ he writes $O_R$. This is what i don't understand.