take an affine base scheme $S=Spec(A)$ with $A$ a complete ring w.r.t. an ideal $I$. Let $X $ a proper scheme over $Spec(A)$. Denote with $Z=\hat{X}$ the formal completion of $X$ w.r.t. $I$.
Let $Y\rightarrow Spf(A)$ be a formal scheme over $Spf(A)$ and assume we have a finite map or a Galois covering with finite Galois group $Y\rightarrow Z$.
Is it true that $Y$ is algebraizable??