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arXiv · 1311.1792

Torsion points and the Lattes family

Laura DeMarco·Xiaoguang Wang·Hexi Ye
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Abstract

We give a dynamical proof of a result of Masser and Zannier [MZ2, MZ3] about torsion points on the Legendre family of elliptic curves. Our methods also treat points of small height. A key ingredient is the arithmetic equidistribution theorem on $\mathbb{P}^1$ of Baker-Rumely, Chambert-Loir, and Favre-Rivera-Letelier. Torsion points on the elliptic curve coincide with preperiodic points for the degree-4 Lattes family of rational functions. Our main new results concern properties of the bifurcation measures for this Lattes family associated to marked points.

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Laura DeMarco, Xiaoguang Wang, Hexi Ye. 2014-10-28. Torsion points and the Lattes family. https://arxiv.org/abs/1311.1792

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