Generic Solutions of Equations Involving the Modular $j$-function
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2022
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866916591069822976 |
|---|---|
| author | Eterović, Sebastian |
| author_facet | Eterović, Sebastian |
| contents | Assuming a modular version of Schanuel's conjecture and the modular Zilber-Pink conjecture, we show that the existence of generic solutions of certain families of equations involving the modular $j$ function can be reduced to the problem of finding a Zariski dense set of solutions. By imposing some conditions on the field of definition of the variety, we are also able to obtain unconditional versions of this result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_12192 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Generic Solutions of Equations Involving the Modular $j$-function Eterović, Sebastian Number Theory Algebraic Geometry Logic 11F03 11J89 Assuming a modular version of Schanuel's conjecture and the modular Zilber-Pink conjecture, we show that the existence of generic solutions of certain families of equations involving the modular $j$ function can be reduced to the problem of finding a Zariski dense set of solutions. By imposing some conditions on the field of definition of the variety, we are also able to obtain unconditional versions of this result. |
| title | Generic Solutions of Equations Involving the Modular $j$-function |
| topic | Number Theory Algebraic Geometry Logic 11F03 11J89 |
| url | https://arxiv.org/abs/2209.12192 |