I am trying to find a reference for the following theorem:
Let $R$ be a complete DVR, and let $Y$ be a scheme projective and flat over $R$. Suppose that $X_0 \longrightarrow Y_0$ is a finite etale morphism, where $Y_0$ is the fiber of $Y$ over the unique closed point of Spec $R$. Then there exists a scheme $X$, finite etale over $Y$, together with a closed immersion $X_0 \longrightarrow X$ such that $X_0 = X \times_Y Y_0$.
In a special case, this allows us to lift etale morphisms in characteristic $p$ to etale morphisms in characteristic zero, and can thus be important in studying the etale fundamental group of varieties in finite characteristic.
Note: While any reference would be appreciated, what I am really interested in is a reference that I can give for attribution purposes. My advisor thinks that this result was proved by Deligne about 40 years ago, but I would like something a little more solid.