Arithmetic diagonal cycles on unitary Shimura varieties

Michael Rapoport; Brian Smithling; Wei Zhang

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arXiv · 1710.06962

Arithmetic diagonal cycles on unitary Shimura varieties

Michael Rapoport·Brian Smithling·Wei Zhang

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Abstract

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.

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Michael Rapoport, Brian Smithling, Wei Zhang. 2017-10-18. Arithmetic diagonal cycles on unitary Shimura varieties. https://arxiv.org/abs/1710.06962

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