A $p$-adic construction of ATR points on $\mathbb{Q}$-curves

Xavier Guitart; Marc Masdeu

A $p$-adic construction of ATR points on $\mathbb{Q}$-curves

Number Theory 2014-09-18 v2

Authors: Xavier Guitart , Marc Masdeu

Abstract

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.

Keywords

elliptic curve ATR point $\mathbb{Q}$-curve $p$-adic construction Heegner point Shimura curve

Cite

@article{arxiv.1402.6531,
  title  = {A $p$-adic construction of ATR points on $\mathbb{Q}$-curves},
  author = {Xavier Guitart and Marc Masdeu},
  journal= {arXiv preprint arXiv:1402.6531},
  year   = {2014}
}

Comments

Final version, accepted in Publicacions Matematiques

A $p$-adic construction of ATR points on $\mathbb{Q}$-curves

Abstract

Keywords

Cite

Comments

Related papers