阿贝尔变种族中不可能相交问题综述

IF 0.8 4区数学 Q2 MATHEMATICS

Expositiones Mathematicae Pub Date : 2023-09-01 DOI:10.1016/j.exmath.2023.04.003

Laura Capuano

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引用次数: 0

摘要

这个简短的调查是我在CMI-HIMR暑期学校上的一门迷你课程的一部分，该课程是关于Zilber - Pink猜想的，Zilber (2002)， Bombieri, Masser和Zannier(1999)在tori的情况下独立表述，Pink(2005)在更一般的混合志村变种的情况下独立表述。在过去的20年里，许多数学家对这个猜想进行了深入的研究，它的一般公式中包含了数论中的许多重要结果。我们将主要在半abel品种和abel品种族的特殊背景下讨论这些问题。

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An overview on problems of Unlikely Intersections in families of abelian varieties

This short survey is part of a minicourse I gave during the CMI-HIMR Summer School “Unlikely Intersections in Diophantine Geometry” on the Zilber–Pink conjecture, formulated independently by Zilber (2002), Bombieri, Masser and Zannier (1999) in the case of tori and by Pink (2005) in the more general setting of mixed Shimura varieties. This conjecture, which includes in its general formulation many important results in number theory, has been intensively studied by several mathematicians in the past 20 years. We will mainly focus on these problems in the special setting of semiabelian varieties and families of abelian varieties.

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来源期刊

Expositiones Mathematicae 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

40 days

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