Cozyleo

We first prove a lemma on generic flatness:

LEMMA (Generic Flatness) Let $A$ be a noetherian domain, and $B$ a finite type $A$-algebra. Let $M$ be a finite $B$-module. Then there exists an $f \in A, f\neq 0$, such that the localization $M_f$ is a free module over $A_f$.

\begin{proof}

Let $K$ be the fraction field of the domain $A$. Consider the localization at this generic point: $M_K = M \otimes K$

\end{proof}