The relative Bogomolov conjecture for fibered products of elliptic curves

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The relative Bogomolov conjecture for fibered products of elliptic curves. / Kühne, Lars.

In: Journal fur die Reine und Angewandte Mathematik, Vol. 2023, No. 795, 2023, p. 243-270.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Kühne, L 2023, 'The relative Bogomolov conjecture for fibered products of elliptic curves', Journal fur die Reine und Angewandte Mathematik, vol. 2023, no. 795, pp. 243-270. https://doi.org/10.1515/crelle-2022-0082

APA

Kühne, L. (2023). The relative Bogomolov conjecture for fibered products of elliptic curves. Journal fur die Reine und Angewandte Mathematik, 2023(795), 243-270. https://doi.org/10.1515/crelle-2022-0082

Vancouver

Kühne L. The relative Bogomolov conjecture for fibered products of elliptic curves. Journal fur die Reine und Angewandte Mathematik. 2023;2023(795):243-270. https://doi.org/10.1515/crelle-2022-0082

Author

Kühne, Lars. / The relative Bogomolov conjecture for fibered products of elliptic curves. In: Journal fur die Reine und Angewandte Mathematik. 2023 ; Vol. 2023, No. 795. pp. 243-270.

Bibtex

@article{2df0059da4724d7b92972aba359d5d90,
title = "The relative Bogomolov conjecture for fibered products of elliptic curves",
abstract = "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 in families of abelian varieties with trivial trace. ",
author = "Lars K{\"u}hne",
note = "Publisher Copyright: {\textcopyright} 2023 Walter de Gruyter GmbH, Berlin/Boston.",
year = "2023",
doi = "10.1515/crelle-2022-0082",
language = "English",
volume = "2023",
pages = "243--270",
journal = "Journal fuer die Reine und Angewandte Mathematik",
issn = "0075-4102",
publisher = "Walterde Gruyter GmbH",
number = "795",

}

RIS

TY - JOUR

T1 - The relative Bogomolov conjecture for fibered products of elliptic curves

AU - Kühne, Lars

N1 - Publisher Copyright: © 2023 Walter de Gruyter GmbH, Berlin/Boston.

PY - 2023

Y1 - 2023

N2 - 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 in families of abelian varieties with trivial trace.

AB - 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 in families of abelian varieties with trivial trace.

U2 - 10.1515/crelle-2022-0082

DO - 10.1515/crelle-2022-0082

M3 - Journal article

AN - SCOPUS:85147206341

VL - 2023

SP - 243

EP - 270

JO - Journal fuer die Reine und Angewandte Mathematik

JF - Journal fuer die Reine und Angewandte Mathematik

SN - 0075-4102

IS - 795

ER -

ID: 371196491