Xinyi Yuan's Publications

The following files may be slightly different from the published versions.

My recent unpublished works:

Quantitativity on the number of rational points in the Mordell conjecture (with Jiawei Yu, Shengxuan Zhou), 2026.
On Vojta's proof of the Mordell conjecture , 2025.
Modular heights of quaternionic Shimura curves, 2022.
The arithmetic Hodge index theorem for adelic line bundles II: finitely generated fields (with Shou-Wu Zhang), 2021.

My works on Arakelov geometry, arithmetic geometry, and arithmetic dynamics:

The geometric Bombieri-Lang conjecture for ramified covers of abelian varieties (with Junyi Xie), to appear in Peking Math. J..
Partial heights, entire curves, and the geometric Bombieri-Lang conjecture (with Junyi Xie), to appear in Acta Math..
Arithmetic bigness and a uniform Bogomolov-type result , Ann. of Math. (2) 203 (2026), no. 1, 15-119.
Adelic line bundles on quasi-projective varieties (with Shou-Wu Zhang), Annals of Mathematics Studies, Princeton University Press, 2026.
Nef cone and successive minima: an example (with Ruoyi Guo), Frontiers in Combinatorics and Number Theory, 2026, 2: 43-54.
Geometric Bogomolov conjecture in arbitrary characteristics (with Junyi Xie), Invent. Math. 229 (2022), no.2, 607-637.
Positivity of Hodge bundles of abelian varieties over some function fields, Compos. Math. 157 (2021), no. 9, 1964-2000.
Effective bounds of linear series on algebraic varieties and arithmetic varieties (with Tong Zhang), J. Reine Angew. Math. 736 (2018), 255-284.
The arithmetic Hodge index theorem for adelic line bundles (with Shou-Wu Zhang), Math. Ann. 367 (2017), no. 3-4, 1123-1171.
Volumes of arithmetic Okounkov bodies, Math. Z. 280 (2015), no. 3-4, 1075--1084.
Relative Noether inequality on fibered surfaces (with Tong Zhang), Adv. Math. 259 (2014), 89-115.
Effective bound of linear series on arithmetic surfaces (with Tong Zhang), Duke Math. J. 162 (2013), no. 10, 1723-1770.
On volumes of arithmetic line bundles II, preprint, 2009.
On volumes of arithmetic line bundles, Compositio Mathematicae 145 (2009), 1447-1464.
Big line bundles over arithmetic varieties, Inventiones Mathematicae 173 (2008), no. 3, 603--649.

My works on automorphic forms, Shimura varieties and L-functions:

Explicit Kodaira-Spencer map over Shimura curves, Acta Math. Sinica (Chinese Ser.) 67 (2024), no. 2, 227-249. (The link here is an English translation of the published Chinese version.)
On the averaged Colmez conjecture (with Shou-Wu Zhang), Ann. of Math. (2) 187 (2018), no. 2, 533-638.
Genus periods, genus Points and congruent Number Problem (with Ye Tian and Shou-Wu Zhang), Asian J. Math. 21 (2017), no. 4, 721-773.
A relative trace formula proof of the Gross--Zagier formula (with Ye Tian and Wei Zhang), in preparation.
The Gross--Zagier formula on Shimura curves (with Shou-Wu Zhang and Wei Zhang), Annals of Mathematics Studies, Princeton University Press, 2012. Please see the erratum.
Triple product L-series and Gross--Schoen cycles (with Shou-Wu Zhang and Wei Zhang), preprint, 2010.
The Gross--Kohnen--Zagier theorem over totally real fields (with Shou-Wu Zhang and Wei Zhang), Compositio Mathematicae 145 (2009), 1147-1162.

My expository works:

Algebraic dynamics, canonical heights and Arakelov geometry, Fifth International Congress of Chinese Mathematicians. Part 1, 2, 893-929, Amer. Math. Soc., Providence, RI, 2012.
On Faltings heights of abelian varieties with complex multiplication, Proceedings of the Seventh International Congress of Chinese Mathematicians, Vol. I, 521-536, Adv. Lect. Math. (ALM), 43, Int. Press, Somerville, MA, 2019.

Last updated: March 2026