17 citations · 65 across the 10 of their papers we have counts for
9 papers · 1 filter
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…
Standard Conjectures and Height Pairings
Shou-Wu Zhang
In this article, we extend Grothendieck's standard conjectures to cycles on degenerated fibers and use them to define some decompositions for the arithmetic Chow group of Gillet--S…
On -adic Waldspurger formula
Yifeng Liu, Shouwu Zhang, Wei Zhang
In this article, we study -adic torus periods for certain -adic valued functions on Shimura curves coming from classical origin. We prove a -adic Waldspurger formula for t…
On the Averaged Colmez Conjecture
Xinyi Yuan, Shou-Wu Zhang
The Colmez conjecture, proposed by Colmez, is a conjecture expressing the Faltings height of a CM abelian variety in terms of some linear combination of logarithmic derivatives of…
Genus Periods, Genus Points and Congruent Number Problem
Ye Tian, Xinyi Yuan, Shouwu Zhang
In this paper, based on an ideal of Tian, we establish a new sufficient condition for a positive integer to be a congruent number in terms of Legendre symbols of prime factors of t…
The arithmetic Hodge index theorem for adelic line bundles I
Xinyi Yuan, Shou-Wu Zhang
This is the first paper of a series. We prove an arithmetic Hodge index theorem for adelic line bundles on projective varieties over number fields. It extends the arithmetic Hodge…