Let (A,m) be a complete local Noetherian ring and let X and Y be two schemes of finite type over A (and flat over A). Let X_{n} and Y_{n} be the reductions of X and Y mod m^{n+1}.

Question: Suppose there is a compatible system of isomorphisms between X_{n}and Y_{n}(for all n). Does there necessarily exist an isomorphism between X and Y over A?

In other words, suppose the formal schemes \hat{X} and \hat{Y} are isomorphic; are X and Y isomorphic?

*Remark*: The answer is `no' if we drop flatness (you can just stick an extra component over the generic fiber) or finite type (A[t] vs. A{t} = the completion of A[t]).