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15 August 2013 Small height and infinite nonabelian extensions
P. Habegger
Duke Math. J. 162(11): 2027-2076 (15 August 2013). DOI: 10.1215/00127094-2331342

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).

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P. Habegger. "Small height and infinite nonabelian extensions." Duke Math. J. 162 (11) 2027 - 2076, 15 August 2013. https://doi.org/10.1215/00127094-2331342

Information

Published: 15 August 2013
First available in Project Euclid: 8 August 2013

zbMATH: 1282.11074
MathSciNet: MR3090783
Digital Object Identifier: 10.1215/00127094-2331342

Subjects:
Primary: 11G50
Secondary: 11G05, 14G40, 14H52

Rights: Copyright © 2013 Duke University Press

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Vol.162 • No. 11 • 15 August 2013
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