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Theorem on formal functions when the initial data is a proper map of formal schemes
Let $\pi: X \to S:=\mathrm{Spf}\text{ } A$ be a proper morphism of $\mathbb{Z}_p$-admissible formal schemes and $\mathcal{F}$ be a coherent sheaf on $X$.
Set $S_0=\{x\}$ be a closed point of $S$ and $...
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