A note on \'etale endomorphisms of normal schemes
Algebraic Geometry
2024-09-24 v2
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.
Keywords
Cite
@article{arxiv.2409.12163,
title = {A note on \'etale endomorphisms of normal schemes},
author = {Lázaro O. Rodríguez Díaz},
journal= {arXiv preprint arXiv:2409.12163},
year = {2024}
}
Comments
Theorem 2 of the previous version is incorrect