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We define variants of PEL type of the Shimura varieties that appear in thecontext of the Arithmetic Gan-Gross-Prasad conjecture. We formulate for them aversion of the AGGP conjecture. We also construct (global and semi-global)integral models of these Shimura varieties and formulate for them conjectureson arithmetic intersection numbers. We prove some of these conjectures in lowdimension.

Arithmetic diagonal cycles on unitary Shimura varieties