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...

Descripción completa

Detalles Bibliográficos
Autores: Guitart, Xavier, Masdeu Sabaté, Marc|||0000-0002-8763-5599
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
Descripción
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.