4 citations · 7 across the 9 of their papers we have counts for
9 papers
Vanishing results for the modified diagonal cycles II: Shimura curves
Congling Qiu, Wei Zhang
We prove vanishing results for the modified diagonal cycles in the Chow groups of the triple products of Shimura curves and their motivic direct summands. In particular we find exa…
Finiteness properties for Shimura curves and modified diagonal cycles
Congling Qiu
We prove that only finitely many Shimura curves can have gonality bounded by a given number, and we study the computability of this finite set. Motivated by the relation between hy…
Vanishing results in Chow groups for the modified diagonal cycles
Congling Qiu, Wei Zhang
We prove a sufficient condition for the vanishing of the modified diagonal cycle in the Chow group (with -coefficients) of the triple product of a curve over $\mathbb{C…
Generic Hecke algebra and theta correspondence over finite fields
Jia-Jun Ma, Congling Qiu, Jialiang Zou
We study the Hecke algebra modules arising from theta correspondence between certain Harish-Chandra series for type I dual pairs over finite fields. For the product of the pair of…
Linearity on ordinary Siegel moduli schemes and joint unlikely almost intersections
Congling Qiu
The goal of this paper is to study a -adic analog of the joint of the conjectures of André--Oort and André--Pink. More precisely, on a product of ordinary Siegel formal moduli s…
Modularity of arithmetic special divisors for unitary Shimura varieties (with an appendix by Yujie Xu)
Congling Qiu
We construct explicit generating series of arithmetic extensions of Kudla's special divisors on integral models of unitary Shimura varieties over CM fields with arbitrary split lev…
Modularity and Heights of CM cycles on Kuga-Sato varieties
Congling Qiu
We prove a higher weight general Gross--Zagier formula for CM cycles on Kuga--Sato varieties over modular curves of arbitrary levels. To formulate and prove this result, we prove s…
The Gross-Zagier-Zhang formula over function fields
Congling Qiu
We prove the Gross-Zagier-Zhang formula over global function fields of arbitrary characteristics. It is an explicit formula which relates the Neron-Tate heights of CM points on abe…
The Manin-Mumford conjecture and the Tate-Voloch conjecture for a product of Siegel moduli spaces
Congling Qiu
We use perfectoid spaces associated to abelian varieties and Siegel moduli spaces to study torsion points and ordinary CM points. We reprove the Manin-Mumford conjecture i.e. Rayna…