Special Points on Fibered Powers of Elliptic Surfaces

Details Special Points on Fibered Powers of Elliptic Surfaces Special Points on Fibered Powers of Elliptic Surfaces

2011-10-10

arxiv.org/abs/1110.1908v1

Mathematics

Number Theory

Scientific paper

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 Andr\'e-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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