Viada, Evelina.
(2008)
* The intersection of a curve with a union of translated codimension-two subgroups in a power of an elliptic curve.*
Algebra and Number Theory, 2 (3).
pp. 249-298.

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## Abstract

Let E be an elliptic curve. An irreducible algebraic curve C embedded in a power A of E is called weak-transverse if it is not contained in any proper algebraic subgroup of A, and transverse if it is not contained in any translate of such a subgroup. Suppose E and C are deﬁned over the algebraic numbers. First we prove that the algebraic points of a transverse curve C that are close to the union of all algebraic subgroups of E g of codimension 2 translated by points in a subgroup G of A of ﬁnite rank are a set of bounded height. The notion of closeness is deﬁned using a height function. If G is trivial, it is sufﬁcient to suppose that C is weak-transverse. The core of the article is the introduction of a method to determine the ﬁnite- ness of these sets. From a conjectural lower bound for the normalized height of a transverse curve C , we deduce that the sets above are ﬁnite. Such a lower bound exists for g ≤ 3. Concerning the codimension of the algebraic subgroups, our results are best possible.

Faculties and Departments: | 05 Faculty of Science |
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UniBasel Contributors: | Viada, Evelina |

Item Type: | Article, refereed |

Article Subtype: | Research Article |

Publisher: | Mathematical Sciences Publishers |

ISSN: | 1937-0652 |

e-ISSN: | 1944-7833 |

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

Language: | English |

Identification Number: | |

edoc DOI: | |

Last Modified: | 15 Nov 2017 08:51 |

Deposited On: | 22 Mar 2012 13:51 |

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