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
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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