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arXiv · 2202.05875

On weakly étale morphisms

Aise Johan de Jong·Noah Olander
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Abstract

We show that the weakly étale morphisms, used to define the pro-étale site of a scheme, are characterized by a lifting property similar to the one which characterizes formally étale morphisms. In order to prove this, we prove a theorem called Henselian descent which is a "Henselized version" of the fact that a scheme defines a sheaf for the fpqc topology. Finally, we show that weakly étale algebras over regular rings arising in geometry are ind-étale and that weakly étale algebras do not always lift along surjective ring homomorphisms.

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Aise Johan de Jong, Noah Olander. 2022-02-11. On weakly étale morphisms. https://arxiv.org/abs/2202.05875

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