Small height and infinite nonabelian extensions

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

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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)
UniBasel Contributors:Habegger, Philipp
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:Duke University Press
Note:Publication type according to Uni Basel Research Database: Journal article
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Last Modified:26 Jan 2018 14:31
Deposited On:26 Jan 2018 14:31

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