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Preprint Number 720

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720. D. Bertrand, D. Masser, A. Pillay, U. Zannier
Relative Manin-Mumford for semi-abelian surfaces.

Submission date: 9 May 2014.


(Updated version of ArXiv.1307.1008v1.)
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.

Mathematics Subject Classification: 14K15, 12H05

Keywords and phrases: semi-abelian varieties; Manin-Mumford, André-Oort and Zilber-Pink conjectures; differential Galois theory; polynomial Pell equations.

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