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math.NT2026
Equidistribution of small points over finitely generated fields
Ruoyi Guo, Lai Shang, Chengyuan Yang +1
We study the equidistribution of small points over finitely generated fields, in connection with a conjecture of Yuan--Zhang. We first give a counterexample showing that numerical…
math.NT2026
Quantitativity in the Mordell Conjecture
Xinyi Yuan
The Mordell conjecture asserts that there are only finitely many rational points on a smooth projective curve of genus at least two over a number field. The uniform Mordell problem…
math.NT2026
Adelic Line Bundles, Arithmetic Positivity and Diophantine Geometry
Xinyi Yuan
This article is an expository account of the basics of adelic line bundles on quasi-projective varieties, arithmetic positivity of adelic line bundles, and applications of positivi…