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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 on

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).

There are also:

  • 4 comment(s) on Section 59.15: The fpqc topology

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