A Buium--Coleman bound for the Mordell--Lang conjecture
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866909678198325248 |
|---|---|
| author | Dogra, Netan Pandit, Sudip |
| author_facet | Dogra, Netan Pandit, Sudip |
| contents | For $X$ a hyperbolic curve of genus $g$ with good reduction at $p\geq 2g$, we give an explicit bound on the Mordell--Lang locus $X(\mathbb{C})\cap Γ$, when $Γ\subset J(\mathbb{C})$ is the divisible hull of a subgroup of $J(\mathbb{Q} _p ^{\mathrm{nr}})$ of rank less than $g$. Without any assumptions on the rank (but with all the other assumptions) we show that $X(\mathbb{C})\cap Γ$ is unramified at $p$, and bound the size of its image in $X(\overline{\mathbb{F} }_p )$. As a corollary, we obtain a new proof that Mordell implies Mordell--Lang for curves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_10155 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Buium--Coleman bound for the Mordell--Lang conjecture Dogra, Netan Pandit, Sudip Number Theory Algebraic Geometry For $X$ a hyperbolic curve of genus $g$ with good reduction at $p\geq 2g$, we give an explicit bound on the Mordell--Lang locus $X(\mathbb{C})\cap Γ$, when $Γ\subset J(\mathbb{C})$ is the divisible hull of a subgroup of $J(\mathbb{Q} _p ^{\mathrm{nr}})$ of rank less than $g$. Without any assumptions on the rank (but with all the other assumptions) we show that $X(\mathbb{C})\cap Γ$ is unramified at $p$, and bound the size of its image in $X(\overline{\mathbb{F} }_p )$. As a corollary, we obtain a new proof that Mordell implies Mordell--Lang for curves. |
| title | A Buium--Coleman bound for the Mordell--Lang conjecture |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2504.10155 |