Explicit lower bounds on the conductors of elliptic curves and abelian varieties over number fields
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866914249326985216 |
|---|---|
| author | Pierre, Tchamitchian |
| author_facet | Pierre, Tchamitchian |
| contents | Following the work of Mestre, we use Weil's explicit formulas to compute explicit lower bounds on the conductors of elliptic curves and abelian varieties over number fields. Moreover, we obtain bounds for the conductor of elliptic curves and abelian varieties over $\mathbb{Q}$ with specified bad reduction and over number fields. As an application, for specific fields, we prove the non-existence of abelian varieties with everywhere good reduction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_12922 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Explicit lower bounds on the conductors of elliptic curves and abelian varieties over number fields Pierre, Tchamitchian Number Theory 11G40, 11F72 (Primary) 11G10, 11G05 (Secondary) Following the work of Mestre, we use Weil's explicit formulas to compute explicit lower bounds on the conductors of elliptic curves and abelian varieties over number fields. Moreover, we obtain bounds for the conductor of elliptic curves and abelian varieties over $\mathbb{Q}$ with specified bad reduction and over number fields. As an application, for specific fields, we prove the non-existence of abelian varieties with everywhere good reduction. |
| title | Explicit lower bounds on the conductors of elliptic curves and abelian varieties over number fields |
| topic | Number Theory 11G40, 11F72 (Primary) 11G10, 11G05 (Secondary) |
| url | https://arxiv.org/abs/2410.12922 |