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.

这篇简短的调查是我在 CMI-HIMR 暑期学校“丢番图几何中不太可能的交集”期间开设的关于 Zilber-Pink 猜想的迷你课程的一部分，由 Zilber (2002)、Bombieri、Masser 和 Zannier (1999) 在该案例中独立制定tori 和 Pink (2005) 在混合 Shimura 品种的更一般的环境中。这个猜想的一般表述包含了数论中的许多重要结果，在过去的 20 年里已经被几位数学家深入研究。我们将主要在半阿贝尔变种和阿贝尔变种科的特殊背景下关注这些问题。