Habegger, Philipp and Pila, Jonathan.
(2012)
* Some unlikely intersections beyond André-Oort.*
Compositio Mathematica, 148 (1).
pp. 1-27.

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Official URL: http://edoc.unibas.ch/51748/

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## Abstract

According to the André–Oort conjecture, an algebraic curve in Y (1)n that is not equal to a special subvariety contains only finitely many points which correspond to ann-tuple of elliptic curves with complex multiplication. Pink’s conjecture generalizes the André–Oort conjecture to the extent that if the curve is not contained in a special subvariety of positive codimension, then it is expected to meet the union of all special subvarieties of codimension two in only finitely many points. We prove this for a large class of curves in Y (1)n. When restricting to special subvarieties of codimension two that are not strongly special we obtain finiteness for all curves defined over Q. Finally, we formulate and prove a variant of the Mordell–Lang conjecture for subvarieties of Y (1)n.

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: | Cambridge University Press |

ISSN: | 0010-437X |

e-ISSN: | 1570-5846 |

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

Identification Number: | |

Last Modified: | 23 Jan 2018 08:53 |

Deposited On: | 23 Jan 2018 08:53 |

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