德林菲尔德模块的𝔭主均匀有界猜想

IF 0.5 3区数学 Q3 MATHEMATICS

International Journal of Number Theory Pub Date : 2024-04-27 DOI:10.1142/s1793042124500611

Shun Ishii

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引用次数: 0

摘要

在本文中，我们研究了关于无性变体扭转的统一有界性猜想的德林费尔德模块类比。结果，我们证明了任意秩的 Drinfeld 模块一维族的𝔭-主均匀有界猜想，这扩展了 Poonen 的一个结果。这一结果可以看作是加多雷-玉川关于无性变体一维族 p 主均匀有界猜想结果的德林费尔德模类似物。

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The 𝔭-primary uniform boundedness conjecture for Drinfeld modules

In this paper, we study a Drinfeld module analogue of the Uniform Boundedness Conjecture on the torsion of abelian varieties. As a result, we prove the $𝔭$ -primary Uniform Boundedness Conjecture for one-dimensional families of Drinfeld modules of arbitrary rank, which extends a result of Poonen. This result can be regarded as a Drinfeld module analogue of the Cadoret–Tamagawa’s result on the $p$ -primary Uniform Boundedness Conjecture for one-dimensional families of abelian varieties.

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来源期刊

International Journal of Number Theory 数学-数学

CiteScore

1.10

自引率

14.30%

发文量

审稿时长

4-8 weeks

期刊介绍： This journal publishes original research papers and review articles on all areas of Number Theory, including elementary number theory, analytic number theory, algebraic number theory, arithmetic algebraic geometry, geometry of numbers, diophantine equations, diophantine approximation, transcendental number theory, probabilistic number theory, modular forms, multiplicative number theory, additive number theory, partitions, and computational number theory.