The Stacks project

Situation 32.4.5. Let $S = \mathop{\mathrm{lim}}\nolimits _{i \in I} S_ i$ be the limit of a directed system of schemes with affine transition morphisms $f_{i'i} : S_{i'} \to S_ i$ (Lemma 32.2.2). We assume that $S_ i$ is quasi-compact and quasi-separated for all $i \in I$. We denote $f_ i : S \to S_ i$ the projection. We also choose an element $0 \in I$.

Comments (2)

Comment #6662 by Jonas Ehrhard on

Maybe observe that is also necessarily quasi-compact and quasi-separated in this situation? Both follows because is affine and is quasi-compact and quasi-separated. Quasi-separatedness is used in 01Z4, quasi-compactness in 01Z5.

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