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Let $X:=Spa A$ be an affinoid adic space, and $\underline X $ the ringed space of $X$. Let $Y:=Spec B$ be an affine scheme, $f: \underline X \longrightarrow Y$ a morphism of ringed spaces.

How to define a morphism of rings $g: B \longrightarrow A$ such that $f$ is induced by $g$?

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What's wrong with the obvious morphism between rings of global sections? –  Jérôme Poineau Apr 29 '13 at 8:35
    
@Jérôme Poineau: the global section of $SpaA$ is $\hat A$, so there is $B \longrightarrow \hat A$. –  kiseki Apr 29 '13 at 13:26
    
Then I am not sure that it is possible to find such a morphism. How would you find $\hat{A} \to A$ that induces $\mathrm{Spa}A \simeq \mathrm{Spa}\hat{A} \to \mathrm{Spec}\hat{A}$? –  Jérôme Poineau Apr 29 '13 at 15:39
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