Special Points on Fibered Powers of Elliptic Surfaces

2011/10/10 by Philipp Habegger, Habegger, Philipp · 1 citation
Mathematics · #11G15 (Primary) 11G18 #11G50 #14G40 #14K22 (Secondary) #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11G15 #msc:11G18 #msc:11G50 #msc:14G40 #msc:14K22

paper · pdf · doi:10.48550/arxiv.1110.1908

arxiv created 2011/10/10 · arxiv updated 2011/10/11

Abstract

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 multiplication. This result can be viewed as a mix of the Manin-Mumford and André-Oort Conjecture and is related to a conjecture of Pink. The main technical tool is a new height inequality. We also use it to give another proof of a case of Gubler's result on the Bogomolov Conjecture over function fields.

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