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Semiabelian varieties and transcendence on Weierstrass sigma functions
Part of
Duc Hiep Pham
Journal:

Glasgow Mathematical Journal , First View

Published online by Cambridge University Press:

25 November 2024, pp. 1-7
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We establish new results on complex and $p$-adic linear independence on a class of semiabelian varieties. As applications, we obtain transcendence results concerning complex and $p$-adic Weierstrass sigma functions associated with elliptic curves.

Relative Manin–Mumford for Semi-Abelian Surfaces
Part of
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
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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.

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