椭圆对数的单一性：一些拓扑方法和有效结果

IF 0.7 3区数学 Q3 MATHEMATICS

Journal of Number Theory Pub Date : 2025-09-05 DOI:10.1016/j.jnt.2025.08.008

Francesco Tropeano

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引用次数: 0

摘要

研究与椭圆型方案相关的单群，通过解析延拓检验了基群对椭圆型方案的作用。我们发展了研究椭圆对数的相对单调群的有效方法，并给出了同时对周期有平凡作用和对对数有非平凡作用的环的显式构造。给出了非扭转截面的相对单群是满秩的一个新的证明。我们的结果包括拓扑方法和有效的技术来分析分支轨迹的部分。

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Monodromy of elliptic logarithms: Some topological methods and effective results

We study monodromy groups associated with elliptic schemes, examining the action induced by the fundamental group of the base via analytic continuation. We develop effective methods for investigating the relative monodromy group of elliptic logarithms and present explicit constructions of loops that simultaneously have trivial action on periods and non-trivial action on logarithms. We provide a new proof that the relative monodromy group of non-torsion sections has full rank. Our results include topological methods and effective techniques for analyzing the ramification locus of sections.

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来源期刊

Journal of Number Theory 数学-数学

CiteScore

1.30

自引率

14.30%

发文量

122

审稿时长

16 weeks

期刊介绍： The Journal of Number Theory (JNT) features selected research articles that represent the broad spectrum of interest in contemporary number theory and allied areas. A valuable resource for mathematicians, the journal provides an international forum for the publication of original research in this field. The Journal of Number Theory is encouraging submissions of quality, long articles where most or all of the technical details are included. The journal now considers and welcomes also papers in Computational Number Theory. Starting in May 2019, JNT will have a new format with 3 sections: JNT Prime targets (possibly very long with complete proofs) high impact papers. Articles published in this section will be granted 1 year promotional open access. JNT General Section is for shorter papers. We particularly encourage submission from junior researchers. Every attempt will be made to expedite the review process for such submissions. Computational JNT . This section aims to provide a forum to disseminate contributions which make significant use of computer calculations to derive novel number theoretic results. There will be an online repository where supplementary codes and data can be stored.