A consequence of the relative Bogomolov conjecture

Dimitrov, Vesselin; Gao, Ziyang; Habegger, Philipp

doi:10.1016/j.jnt.2021.03.028

Journal of Number Theory

2022

DOI: 10.1016/j.jnt.2021.03.028

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A consequence of the relative Bogomolov conjecture

Vesselin Dimitrov¹,

Ziyang Gao

Philipp Habegger

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2023

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The relative Bogomolov conjecture for fibered products of elliptic curves

Kühne

2023

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

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We deduce an analogue of the Bogomolov conjecture for non-degenerate subvarieties in fibered products of families of elliptic curves from the author’s recent theorem on equidistribution in families of abelian varieties. This generalizes results of DeMarco and Mavraki and improves certain results of Manin–Mumford type proven by Masser and Zannier to results of Bogomolov type, yielding the first results of this type for subvarieties of relative dimension > 1 {>1} in families of abelian varieties with trivial trace.

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The relative Bogomolov conjecture for fibered products of elliptic curves

Kühne

2023

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

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A consequence of the relative Bogomolov conjecture

Cited by 1 publication

References 22 publications

The relative Bogomolov conjecture for fibered products of elliptic curves

The relative Bogomolov conjecture for fibered products of elliptic curves

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