80 citations · 162 across the 21 of their papers we have counts for
24 papers
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…
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…
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…
The Geometric Bombieri-Lang Conjecture for Ramified Covers of Abelian Varieties
Junyi Xie, Xinyi Yuan
In this paper, we prove the geometric Bombieri-Lang conjecture for projective varieties which have finite morphisms to abelian varieties of trivial traces over function fields of c…
Partial Heights, Entire Curves, and the Geometric Bombieri-Lang Conjecture
Junyi Xie, Xinyi Yuan
We introduce a new approach to the geometric Bombieri--Lang conjecture for hyperbolic varieties in characteristic 0. The main idea is to construct an entire curve on a special fibe…
Modular Heights of Quaternionic Shimura Curves
Xinyi Yuan
The goal of this paper is to prove a formula expressing the modular height of a quaternionic Shimura curve over a totally real number field in terms of the logarithmic derivative o…