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math.NT2024
Hodge cycles and quadratic relations between holomorphic periods on CM abelian varieties
Ziyang Gao, Emmanuel Ullmo
In this paper, we prove the following result advocating the importance of monomial quadratic relations between holomorphic CM periods. For any simple CM abelian variety , we can…
math.NT2024
Heights of Ceresa and Gross-Schoen cycles
Ziyang Gao, Shou-Wu Zhang
We study the Beilinson-Bloch heights of Ceresa and Gross-Schoen cycles in families. We construct that for any , a Zariski open dense subset o…
math.NT2024
Bi--structures on Hermitian symmetric spaces and quadratic relations between CM periods
Ziyang Gao, Emmanuel Ullmo, Andrei Yafaev
In this paper, we introduce the notion of a bi--structure on the tangent space at a CM point on a locally Hermitian symmetric domain. We prove that this bi-$…