Remark 35.8.3 (03FG)—The Stacks project

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Part 2: Schemes
Chapter 35: Descent
Section 35.8: Quasi-coherent sheaves and topologies, I
Remark 35.8.3 (cite)

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Remark 35.8.3. In Topologies, Lemma 34.3.12 we have seen that the small Zariski site of a scheme $S$ is equivalent to $S$ as a topological space in the sense that the categories of sheaves are naturally equivalent. Now that $S_{Zar}$ is also endowed with a structure sheaf $\mathcal{O}$ we see that sheaves of modules on the ringed site $(S_{Zar}, \mathcal{O})$ agree with sheaves of modules on the ringed space $(S, \mathcal{O}_ S)$ .

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