Proof of Miyanishi's conjecture on endomorphisms of varieties
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914336301121536 |
|---|---|
| author | Sarkar, Supravat |
| author_facet | Sarkar, Supravat |
| contents | If $X$ is a quasi-projective variety over a field $k$ and $ϕ$ a birational endomorphism of $X$ that is injective outside a closed subset of codimension $\geq 2$, we prove that $ϕ$ is an automorphism. This generalizes an old theorem of Ax and proves a conjecture of Miyanishi. A key step in our proof is a finiteness result on class groups, which is of interest in its own right. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_16168 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Proof of Miyanishi's conjecture on endomorphisms of varieties Sarkar, Supravat Algebraic Geometry 14B05, 14C22 If $X$ is a quasi-projective variety over a field $k$ and $ϕ$ a birational endomorphism of $X$ that is injective outside a closed subset of codimension $\geq 2$, we prove that $ϕ$ is an automorphism. This generalizes an old theorem of Ax and proves a conjecture of Miyanishi. A key step in our proof is a finiteness result on class groups, which is of interest in its own right. |
| title | Proof of Miyanishi's conjecture on endomorphisms of varieties |
| topic | Algebraic Geometry 14B05, 14C22 |
| url | https://arxiv.org/abs/2602.16168 |