On Vojta's proof of the Mordell conjecture

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This is a Quantitative Study study.

Xinyi Yuan

doi:10.48550/arxiv.2508.11888

August 16, 2025Open Access

On Vojta's proof of the Mordell conjecture

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Key Points

Vojta's proof provides a new framework for understanding the mordell conjecture, linking it to Arakelov geometry.
The analysis replaces Gillet--Soule's theorem with Yuan's arithmetic Siu inequality, marking a significant methodological shift.
This reorganization clarifies aspects of Faltings' theorem, highlighting the role of Arakelov geometry in modern number theory.
Implications for future research may emerge from this new perspective, influencing how similar conjectures are approached.

Implication

Analysis reinterprets Vojta's insights on the Mordell conjecture, suggesting that Yuan's arithmetic Siu inequality enhances existing proofs.

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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Cite This Study

Xinyi Yuan (2025) studied this question.

synapsesocial.com/papers/68d6e16f8b2b6861e4c401f8 https://doi.org/10.48550/arxiv.2508.11888

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On Vojta's proof of the Mordell conjecture

Key Points

Implication

Abstract

Discussion

Cite This Study

On Vojta's proof of the Mordell conjecture

Key Points

Implication

Abstract

Discussion

Cite This Study

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