椭圆曲线纤维制品的相对Bogomolov猜想

IF 1.2 1区数学 Q1 MATHEMATICS

Journal fur die Reine und Angewandte Mathematik Pub Date : 2023-01-27 DOI:10.1515/crelle-2022-0082

L. Kühne

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引用次数: 0

摘要

摘要本文从作者最近的关于阿贝尔变异族的等分布定理出发，推导出椭圆曲线族纤维积中非退化子变异的Bogomolov猜想的一个类似。这将DeMarco和Mavraki的结果推广，并将Masser和Zannier证明的Manin-Mumford型的某些结果改进为Bogomolov型的结果，在具有平凡迹的阿贝尔变种族中，对于相对维数>1{>1}的子变种，得到了该类型的第一个结果。

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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 {>1} in families of abelian varieties with trivial trace.

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来源期刊

Journal fur die Reine und Angewandte Mathematik 数学-数学

CiteScore

2.50

自引率

6.70%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal für die reine und angewandte Mathematik is the oldest mathematics periodical still in existence. Founded in 1826 by August Leopold Crelle and edited by him until his death in 1855, it soon became widely known under the name of Crelle"s Journal. In the almost 180 years of its existence, Crelle"s Journal has developed to an outstanding scholarly periodical with one of the worldwide largest circulations among mathematics journals. It belongs to the very top mathematics periodicals, as listed in ISI"s Journal Citation Report.