Definition 87.9.9. Let $S$ be a scheme. Let $A$ be a weakly admissible topological ring over $S$, see Definition 87.4.8^{1}. The *formal spectrum* of $A$ is the affine formal algebraic space

where the colimit is over the set of weak ideals of definition of $A$ and taken in the category $\mathop{\mathit{Sh}}\nolimits ((\mathit{Sch}/S)_{fppf})$.

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