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math.NT2019★ 1 cited
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…
math.AG2019
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…