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arXiv · 2104.03431

Recent developments of the Uniform Mordell-Lang Conjecture

Ziyang Gao
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Abstract

This expository survey is based on my online talk at the ICCM 2020. It aims to sketch key steps of the recent proof of the uniform Mordell-Lang conjecture for curves embedded into Jacobians (a question of Mazur). The full version of this conjecture is proved by combining Dimitrov-Gao-Habegger (https://annals.math.princeton.edu/articles/17715) and K\"{u}hne (arXiv:2101.10272). We include in this survey a detailed proof on how to combine these two results, which was implicitly done in another short paper of Dimitrov-Gao-Habegger (arXiv:2009.08505) but not explicitly written in existing literature. At the end of the survey we state some future aspects.

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Ziyang Gao. 2021-04-07. Recent developments of the Uniform Mordell-Lang Conjecture. https://arxiv.org/abs/2104.03431

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