Abstract
We show that every unramified morphism \({X\to Y}\) has a canonical and universal factorization \({X\hookrightarrow E_{X/Y}\to Y}\) where the first morphism is a closed embedding and the second is étale (but not separated).
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Rydh, D. The canonical embedding of an unramified morphism in an étale morphism. Math. Z. 268, 707–723 (2011). https://doi.org/10.1007/s00209-010-0691-8
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DOI: https://doi.org/10.1007/s00209-010-0691-8