Situation 70.23.1. Let $S$ be a scheme, for example $\mathop{\mathrm{Spec}}(\mathbf{Z})$. Let $B = \mathop{\mathrm{lim}}\nolimits _{i \in I} B_ i$ be the limit of a directed inverse system of Noetherian spaces over $S$ with affine transition morphisms $B_{i'} \to B_ i$ for $i' \geq i$.

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