Lemma 98.27.10 (0GHG)—The Stacks project

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Part 7: Algebraic Stacks
Chapter 98: Artin's Axioms
Section 98.27: Artin's theorem on contractions
Lemma 98.27.10 (cite)

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Lemma 98.27.10. In Situation 98.27.1 the functor $F$ satisfies the sheaf property for all étale coverings of locally Noetherian schemes over $S$ .

Proof. Omitted. Hint: morphisms may be defined étale locally. $\square$

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