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math.NT2026
Quantitativity on the number of rational points in the Mordell conjecture
Jiawei Yu, Xinyi Yuan, Shengxuan Zhou
In this paper, we prove an explicit upper bound on the number of rational points on a smooth projective curve of genus at least two over a number field. This gives explicit constan…
math.NT2025
On Vojta's proof of the Mordell conjecture
Xinyi Yuan
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--Sou…