Lemma 66.20.5 (04KC)—The Stacks project

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Table of contents
Part 4: Algebraic Spaces
Chapter 66: Properties of Algebraic Spaces
Section 66.20: Supports of abelian sheaves
Lemma 66.20.5 (cite)

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Lemma 66.20.5. The support of a sheaf of rings on the small étale site of an algebraic space is closed.

Proof. This is true because (according to our conventions) a ring is $0$ if and only if $1 = 0$ , and hence the support of a sheaf of rings is the support of the unit section. $\square$

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