Remark 59.15.9 (03O4)—The Stacks project

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Table of contents
Part 3: Topics in Scheme Theory
Chapter 59: Étale Cohomology
Section 59.15: The fpqc topology
Remark 59.15.9 (cite)

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Remark 59.15.9. The fpqc is finer than the Zariski, étale, smooth, syntomic, and fppf topologies. Hence any presheaf satisfying the sheaf condition for the fpqc topology will be a sheaf on the Zariski, étale, smooth, syntomic, and fppf sites. In particular representable presheaves will be sheaves on the étale site of a scheme for example.

Comments (2)

Comment #5417 by David Roberts on July 24, 2020 at 01:59

There is now the v-topology, which is finer than fpqc, so this Remark is no longer true (though maybe the v-topology doesn't get much exposure).

Comment #5644 by Johan on November 14, 2020 at 16:16

Thanks and fixed here.

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