Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2409.12163 |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866912040925265920 |
|---|---|
| author | Díaz, Lázaro O. Rodríguez |
| author_facet | Díaz, Lázaro O. Rodríguez |
| contents | We prove that under some extra hypothesis, given an étale 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 étale cover out of a surjective étale morphism. We show that in some cases the surjectivity hypothesis can be removed if the intended étale cover is Galois. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_12163 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on étale endomorphisms of normal schemes Díaz, Lázaro O. Rodríguez Algebraic Geometry We prove that under some extra hypothesis, given an étale 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 étale cover out of a surjective étale morphism. We show that in some cases the surjectivity hypothesis can be removed if the intended étale cover is Galois. |
| title | A note on étale endomorphisms of normal schemes |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2409.12163 |