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arXiv · 2409.12163

A note on \'etale endomorphisms of normal schemes

Lázaro O. Rodríguez Díaz
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Abstract

We prove that under some extra hypothesis, given an \'etale endomorphism of a normal irreducible Noetherian and simply connected scheme, if the endomorphism is surjective then it is injective. The additional assumption concerns the possibility of constructing an \'etale cover out of a surjective \'etale morphism. We show that in some cases the surjectivity hypothesis can be removed if the intended \'etale cover is Galois.

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Lázaro O. Rodríguez Díaz. 2024-09-18. A note on \'etale endomorphisms of normal schemes. https://arxiv.org/abs/2409.12163

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