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arXiv · 2108.05625

Arithmetic bigness and a uniform Bogomolov-type result

Xinyi Yuan
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Abstract

In this paper, we prove that the admissible canonical bundle of the universal family of curves is a big adelic line bundle, and apply it to prove a uniform Bogomolov-type theorem for curves over global fields of all characteristics. This gives a different approach to the uniform Mordell-Lang type of result of Dimitrov-Gao-Habegger and Kuhne. The treatment is based on the recent theory of adelic line bundles of Yuan-Zhang.

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Xinyi Yuan. 2021-08-12. Arithmetic bigness and a uniform Bogomolov-type result. https://arxiv.org/abs/2108.05625

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