# does analytic finite over algebraic implies algebraic?

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??

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Perhaps this is better suited for mathoverflow. Just my opinion. – Martin Brandenburg Mar 28 '12 at 20:41