We define variants of PEL type of the Shimura varieties that appear in the context of the Arithmetic Gan-Gross-Prasad conjecture. We formulate for them a version of the AGGP conjecture. We also construct (global and semi-global) integral models of these Shimura varieties and formulate for them conjectures on arithmetic intersection numbers. We prove some of these conjectures in low dimension.

中文翻译：

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酉 Shimura 簇的算术对角圈

我们定义了出现在算术 Gan-Gross-Prasad 猜想中的 Shimura 变体的 PEL 类型变体。我们为他们制定了 AGGP 猜想的一个版本。我们还构建了这些 Shimura 变体的（全局和半全局）积分模型，并为它们制定了对算术交集数的猜想。我们在低维中证明了这些猜想中的一些。