Lemma 61.3.6 (096J)—The Stacks project

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Part 3: Topics in Scheme Theory
Chapter 61: Pro-étale Cohomology
Section 61.3: Local isomorphisms
Lemma 61.3.6 (cite)

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Lemma 61.3.6. Let $A \to B$ be a local isomorphism. Then there exist $n \geq 0$ , $g_1, \ldots , g_ n \in B$ , $f_1, \ldots , f_ n \in A$ such that $(g_1, \ldots , g_ n) = B$ and $A_{f_ i} \cong B_{g_ i}$ .

Proof. Omitted. $\square$

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