P. Habegger

activity

20112026

most citedSmall Height and Infinite Non-Abelian Extensions

35 citations · 93 across the 19 of their papers we have counts for

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Showing 2011Show all

3 papers · 1 filter

math.NT2011

Special Points on Fibered Powers of Elliptic Surfaces

Philipp Habegger

Consider a fibered power of an elliptic surface. We characterize its subvarieties that contain a Zariski dense set of points that are torsion points in fibers with complex multipli…

math.NT2011★ 35 cited

Small Height and Infinite Non-Abelian Extensions

Philipp Habegger

Let $E$ be an elliptic curve defined over the rationals without complex multiplication. The field $F$ generated by all torsion points of $E$ is an infinite, non-abelian Galois exte…

math.NT2011

Torsion Points on Elliptic Curves in Weierstrass Form

Philipp Habegger

We prove that there are only finitely many complex numbers $a$ and $b$ with $4 a^{3} + 27 b^{2} \neq = 0$ such that the three points $(1, *), (2, *),$ and $(3, *)$ are simultaneously torsion on t…