Exercise 111.51.3. Suppose that $X \to \mathop{\mathrm{Spec}}(R)$ is a proper morphism and that $R$ is a discrete valuation ring with residue field $k$. Suppose that $X \times _{\mathop{\mathrm{Spec}}(R)} \mathop{\mathrm{Spec}}(k)$ is the empty scheme. Show that $X$ is the empty scheme.

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