Question

Hi, I found the following in the proof of a theorem: $ Z \subset Y \times M$ where $M$ is a smooth projective variety over $\mathbb{C}$, $Y$ is a scheme and $Z$ is a subscheme of the product, flat over $Y$. Then $\mathcal{O}_Z$ is of finite homological dimension (is quasi-isomorphic to a bounded complex of locally free sheaves), as an $\mathcal{O}_{ Y \times M}$-module. Why? (all schemes are of finite type over $\mathbb{C}$) Thank you.