Lemma 61.12.5. Let $T$ be an affine scheme. Let $\{ T_ i \to T\} _{i \in I}$ be a pro-étale covering of $T$. Then there exists a pro-étale covering $\{ U_ j \to T\} _{j = 1, \ldots , n}$ which is a refinement of $\{ T_ i \to T\} _{i \in I}$ such that each $U_ j$ is an affine scheme. Moreover, we may choose each $U_ j$ to be open affine in one of the $T_ i$.

Proof. This follows directly from the definition. $\square$

There are also:

• 4 comment(s) on Section 61.12: The pro-étale site

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).