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D. Bertrand, D. Masser, A. Pillay, U. Zannier
Journal: Proceedings of the Edinburgh Mathematical Society / Volume 59 / Issue 4 / November 2016
Published online by Cambridge University Press: 18 January 2016, pp. 837-875
Print publication: November 2016
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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 4, as well as the study of polynomial Pell equations with non-separable discriminants.

Interpolation on algebraic groups
S. Fischler
Journal: Compositio Mathematica / Volume 141 / Issue 4 / July 2005
Published online by Cambridge University Press: 21 June 2005, pp. 907-925
Print publication: July 2005
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We prove an interpolation lemma with multiplicities on a commutative algebraic group. This statement is ‘dual’ to zero estimates used in transcendental number theory. The special case where no multiplicities are involved has been proved by Masser.