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Arithmetic diagonal cycles on unitary Shimura varieties

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arxiv 1710.06962 v6 pith:A53NNS6J submitted 2017-10-18 math.NT math.AGmath.RT

Michael Rapoport , Brian Smithling , Wei Zhang This is my paper · ORCID
classification math.NTmath.AGmath.RT
keywords arithmeticshimuravarietiesconjectureconjecturesformulatethemaggp
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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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  1. Weil representation and Arithmetic Fundamental Lemma

    math.NT 2019-09 conditional novelty 8.0 of 10

    A global proof of the arithmetic fundamental lemma for unitary groups over Q_p (odd p >= n) via an SL_2-equivariant relative trace formula and derived CM cycles, which also yields the Jacquet-Rallis fundamental lemma ...

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