3 papers
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…
math.NT2025
Adelic line bundles on quasi-projective varieties
Xinyi Yuan, Shou-Wu Zhang
In this book, we establish a theory of adelic line bundles over quasi-projective varieties over finitely generated fields. Besides definitions of adelic line bundles, we consider t…