Habegger, Philipp.
(2013)
* Small height and infinite nonabelian extensions.*
Duke Mathematical Journal, 162 (11).
pp. 2027-2076.

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Official URL: http://edoc.unibas.ch/51745/

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## Abstract

Let E be an elliptic curve defined over Q without complex multiplication. The field F generated over Q by all torsion points of E is an infinite, nonabelian Galois extension of the rationals which has unbounded, wild ramification above all primes. We prove that the absolute logarithmic Weil height of an element of F is either zero or bounded from below by a positive constant depending only on E. We also show that the Néron–Tate height has a similar gap on E(F) and use this to determine the structure of the group E(F).

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: | Duke University Press |

ISSN: | 0012-7094 |

e-ISSN: | 1547-7398 |

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

Identification Number: | |

Last Modified: | 26 Jan 2018 14:31 |

Deposited On: | 26 Jan 2018 14:31 |

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