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arXiv · 1910.14122

Uniformity of fibres of period mappings and the $S$-unit equation

Brett Nasserden·Stanley Yao Xiao
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Abstract

In this paper we give a refinement of the method introduced by Lawrence and Venkatesh and thereby showing that their proof of Mordell's conjecture is uniform up to a uniform bound on the number of Galois representations attached to some family of abelian varieties. We are also able to give an unconditional proof of a uniform boundedness statement on the number of solutions to $S$-unit equations, which qualitatively is best possible, recovering a result of Evertse.

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Brett Nasserden, Stanley Yao Xiao. 2019-10-30. Uniformity of fibres of period mappings and the $S$-unit equation. https://arxiv.org/abs/1910.14122

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