Habegger, Philipp.
(2010)
* Weakly bounded height on modular curves.*
Acta Mathematica Vietnamica, 35 (1).
pp. 43-69.

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## Abstract

We study the intersection of a ﬁxed plane algebraic curve C with modular curves of varying level. The height of points in such intersections cannot be bounded from above independently of the level when C is deﬁned over the ﬁeld of algebraic numbers. But we ﬁnd a certain class of curves C for which the height is bounded logarithmically in the level. This bound is strong enough to imply certain ﬁniteness result. Such evidence leads to a conjecture involving a logarithmic height bound unless C is of so-called special type. We also discuss connections to recent progress on conjectures concerning unlikely intersections.

Faculties and Departments: | 05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Zahlentheorie (Habegger) |
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UniBasel Contributors: | Habegger, Philipp |

Item Type: | Article, refereed |

Article Subtype: | Research Article |

Publisher: | Institute of Mathematics |

ISSN: | 0251-4184 |

e-ISSN: | 2315-4144 |

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

Language: | English |

Related URLs: | |

Last Modified: | 15 Jan 2018 09:01 |

Deposited On: | 15 Jan 2018 09:01 |

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