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arXiv · 1307.1008

Relative Manin-Mumford for semi-abelian surfaces

Daniel Bertrand·David Masser·Anand Pillay·Umberto Zannier
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Abstract

We show that Ribet sections are the only obstruction to the validity of the relative Manin-Mumford conjecture for one dimensional families of semi-abelian surfaces. Applications include special cases of the Zilber-Pink conjecture for curves in a mixed Shimura variety of dimension four, as well as the study of polynomial Pell equations with non-separable discriminants.

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Daniel Bertrand, David Masser, Anand Pillay, Umberto Zannier. 2013-07-03. Relative Manin-Mumford for semi-abelian surfaces. https://arxiv.org/abs/1307.1008

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