Relative Manin-Mumford for semi-abelian surfaces

2013/07/03 by Bertrand, Daniel, Masser, David, Pillay, Anand +1 · 1 citation
#11J95 #12H05 #14K15 #14K20 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1307.1008

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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• Unlikely intersections in Shimura varieties and beyond: a survey

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