On weakly étale morphisms
| Authors |
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|---|---|
| Publication date | 03-2024 |
| Journal | Journal of Pure and Applied Algebra |
| Article number | 107532 |
| Volume | Issue number | 228 | 3 |
| Number of pages | 9 |
| Organisations |
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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. |
| Document type | Article |
| Language | English |
| Published at | https://doi.org/10.1016/j.jpaa.2023.107532 |
| Other links | https://www.scopus.com/pages/publications/85172804055 |
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On weakly étale morphisms
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