4 citations · 7 across the 9 of their papers we have counts for
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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…
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…