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2015 A $p$-adic construction of ATR points on $\mathbb{Q}$-curves
Xavier Guitart, Marc Masdeu
Publ. Mat. 59(2): 511-545 (2015).


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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Xavier Guitart. Marc Masdeu. "A $p$-adic construction of ATR points on $\mathbb{Q}$-curves." Publ. Mat. 59 (2) 511 - 545, 2015.


Published: 2015
First available in Project Euclid: 30 July 2015

zbMATH: 06470491
MathSciNet: MR3374616

Primary: 11G05
Secondary: 11G18 , 11Y50

Keywords: Algebraic points on elliptic curves , ATR points , Heegner points

Rights: Copyright © 2015 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.59 • No. 2 • 2015
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