Proposition 32.5.4. Let $S$ be a quasi-compact and quasi-separated scheme. There exist a directed set $I$ and an inverse system of schemes $(S_ i, f_{ii'})$ over $I$ such that

the transition morphisms $f_{ii'}$ are affine

each $S_ i$ is of finite type over $\mathbf{Z}$, and

$S = \mathop{\mathrm{lim}}\nolimits _ i S_ i$.

## Comments (0)