Adelic Mordell-Lang and the Brauer-Manin obstruction
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917050067189760 |
|---|---|
| author | Creutz, Brendan |
| author_facet | Creutz, Brendan |
| contents | Let $X$ be a closed subvariety of an abelian variety $A$ over a global function field $k$ such that the base change of $A$ to an algebraic closure does not have any positive dimensional isotrivial quotient. We prove that every adelic point on $X$ which is the limit of a sequence of $k$-rational points on $A$ is a limit of $k$-rational points on $X$. Assuming finiteness of the Tate-Shafarevich group of $A$, this implies that the rational points on $X$ are dense in the Brauer set of $X$. Similar results are obtained over totally imaginary number fields, conditionally on an adelic Mordell-Lang conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_25931 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Adelic Mordell-Lang and the Brauer-Manin obstruction Creutz, Brendan Number Theory Algebraic Geometry Let $X$ be a closed subvariety of an abelian variety $A$ over a global function field $k$ such that the base change of $A$ to an algebraic closure does not have any positive dimensional isotrivial quotient. We prove that every adelic point on $X$ which is the limit of a sequence of $k$-rational points on $A$ is a limit of $k$-rational points on $X$. Assuming finiteness of the Tate-Shafarevich group of $A$, this implies that the rational points on $X$ are dense in the Brauer set of $X$. Similar results are obtained over totally imaginary number fields, conditionally on an adelic Mordell-Lang conjecture. |
| title | Adelic Mordell-Lang and the Brauer-Manin obstruction |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2510.25931 |