The hybrid conjecture holds for the universal abelian scheme A_g over A_g, encompassing André-Oort, André-Pink-Zannier, mixed André-Oort, and Manin-Mumford conjectures for abelian varieties.
Faltings, Diophantine approximation on abelian varieties , Ann
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Shows that sets of representatives of grand (f,K)-orbits are Zariski dense for endomorphisms on all abelian varieties over number fields, assuming existence of a dense orbit point.
Survey presenting the quantitative uniformity theorem for the Mordell conjecture proved by Yu--Yuan--Zhou, building on Vojta, Dimitrov--Habegger--Gao and Kuhne.
citing papers explorer
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Hybrid Conjecture in a Mixed Shimura variety
The hybrid conjecture holds for the universal abelian scheme A_g over A_g, encompassing André-Oort, André-Pink-Zannier, mixed André-Oort, and Manin-Mumford conjectures for abelian varieties.
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On Dense Orbit Transversality for Endomorphisms of Abelian Varieties
Shows that sets of representatives of grand (f,K)-orbits are Zariski dense for endomorphisms on all abelian varieties over number fields, assuming existence of a dense orbit point.
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Quantitativity in the Mordell Conjecture
Survey presenting the quantitative uniformity theorem for the Mordell conjecture proved by Yu--Yuan--Zhou, building on Vojta, Dimitrov--Habegger--Gao and Kuhne.