Small height and infinite nonabelian extensions

By P. Habegger. 2011

58 citations recorded by the source corpus.

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 Neron–Tate height has a similar gap on E(F) and use this to determine the structure of the group E(F).

Subfields: Geometry and Topology, Information Systems, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0ce0c2c39b8dc1d40ed529a07741887668aa2e64

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In Geometry and Topology

1. Umberto Zannier
2. Jonathan Pila
3. P. Habegger
4. Aaron Levin
5. Ziyang Gao
6. D. Masser
7. Fabrizio Barroero
8. Joseph H. Silverman

In Mathematical Physics

1. Umberto Zannier
2. Aaron Levin

Citations in the corpus

• On fields with the Property (B) (2014, background): “A third family has been recently exhibited by Habegger [Hab].”