On Vojta's proof of the Mordell conjecture

Xinyi Yuan

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arXiv · 2508.11888

On Vojta's proof of the Mordell conjecture

Xinyi Yuan

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Abstract

This paper re-organizes Vojta's proof of the Mordell conjecture (i.e. Faltings' theorem) in terms of Arakelov geometry. A new ingredient is to replace an application of Gillet--Soule's arithmetic Riemannn--Roch theorem by that of Yuan's arithmetic Siu inequality.

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Xinyi Yuan. 2025-08-16. On Vojta's proof of the Mordell conjecture. https://arxiv.org/abs/2508.11888

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