Let $S$ be a scheme, and $X$, $Y$ be two schemes that are étale and finite of same degree $N\geq 1$ over $S$. Let $f:X\rightarrow Y$ be a surjective morphism of schemes over $S$. Is it true that $f$ is then an isomorphism of $S$-scheme? If so, could someone please provide a hint or a reference for the proof?
I thank you very much for you help.