Lemma 59.33.3 (04HY)—The Stacks project

Table of contents
Part 3: Topics in Scheme Theory
Chapter 59: Étale Cohomology
Section 59.33: Stalks of the structure sheaf
Lemma 59.33.3 (cite)

Lemma 59.33.3. Let $S$ be a scheme. Let $s \in S$. Then we have

\[ \mathcal{O}_{S, s}^ h = \mathop{\mathrm{colim}}\nolimits _{(U, u)} \mathcal{O}(U) \]

where the colimit is over the filtered category of étale neighbourhoods $(U, u)$ of $(S, s)$ such that $\kappa (s) = \kappa (u)$.

Proof. This lemma is a copy of More on Morphisms, Lemma 37.35.5. $\square$

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