Barroero, Fabrizio.
(2017)
* CM relations in fibered powers of elliptic families.*
Journal of the Institute of Mathematics of Jussieu, 18 (5).
pp. 941-956.

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Official URL: https://edoc.unibas.ch/59228/

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## Abstract

Let $E_\lambda$ be the Legendre family of elliptic curves. Given $n$ linearly independent points $P_1,\dots , P_n \in E_\lambda\left(\overline{\mathbb{Q}(\lambda)}\right)$ we prove that there are at most finitely many complex numbers $\lambda_0$ such that $E_{\lambda_0} $ has complex multiplication and $P_1(\lambda_0), \dots ,P_n(\lambda_0)$ are dependent over $End(E_{\lambda_0})$. This implies a positive answer to a question of Bertrand and, combined with a previous work in collaboration with Capuano, proves the Zilber-Pink conjecture for a curve in a fibered power of an elliptic scheme when everything is defined over $\overline{\mathbb{Q}}$.

Faculties and Departments: | 05 Faculty of Science 05 Faculty of Science > Departement Mathematik und Informatik 05 Faculty of Science > Departement Mathematik und Informatik > Mathematik |
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UniBasel Contributors: | Barroero, Fabrizio |

Item Type: | Article, refereed |

Article Subtype: | Research Article |

Publisher: | Cambridge University Press |

ISSN: | 1474-7480 |

e-ISSN: | 1475-3030 |

Note: | Publication type according to Uni Basel Research Database: Journal article |

Identification Number: | |

Last Modified: | 28 Jul 2020 13:11 |

Deposited On: | 24 Jul 2020 14:50 |

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