A p-adic construction of ATR points on Q-curves
In this note we consider certain elliptic curves defined over real quadratic fields isogenous to their Galois conjugate. We give a construction of algebraic points on these curves defined over almost totally real number fields. The main ingredient is the system of Heegner points arising from Shimura...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2015 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:133145 |
| Acceso en línea: | https://ddd.uab.cat/record/133145 https://dx.doi.org/urn:doi:10.5565/PUBLMAT_59215_09 |
| Access Level: | acceso abierto |
| Palabra clave: | Algebraic points on elliptic curves ATR points Heegner points |
| Sumario: | In this note we consider certain elliptic curves defined over real quadratic fields isogenous to their Galois conjugate. We give a construction of algebraic points on these curves defined over almost totally real number fields. The main ingredient is the system of Heegner points arising from Shimura curve uniformizations. In addition, we provide an explicit p-adic analytic formula which allows for the effective, algorithmic calculation of such points. |
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