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Modularity of generating series of divisors on unitary Shimura varieties II: arithmetic applications

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arxiv 1710.00628 v2 pith:3WL35KCC submitted 2017-10-02 math.NT math.AG

Jan Bruinier , Benjamin Howard , Stephen S. Kudla , Michael Rapoport , Tonghai Yang This is my paper · ORCID
classification math.NTmath.AG
keywords shimuraunitaryvarietiesarithmeticdivisorsgeneratingmodularityprove
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We prove two formulas in the style of the Gross-Zagier theorem, relating derivatives of L-functions to arithmetic intersection pairings on a unitary Shimura variety. We also prove a special case of Colmez's conjecture on the Faltings heights of abelian varieties with complex multiplication. These results are derived from the authors' earlier results on the modularity of generating series of divisors on unitary Shimura varieties.

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  1. Remarks on generating series for special cycles

    math.NT 2019-08 conditional novelty 7.0 of 10

    Assuming the Bloch-Beilinson conjecture, the Chow group valued generating series for special cycles on orthogonal Shimura varieties over totally real fields is modular in all codimensions and for all d_+.

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