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Modularity of generating series of divisors on unitary Shimura varieties

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arxiv 1702.07812 v3 pith:XKNDWYAF submitted 2017-02-25 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 groupchowdivisorsgeneratingintegralmodelmodularityseries
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We form generating series of special divisors, valued in the Chow group and in the arithmetic Chow group, on the compactified integral model of a Shimura variety associated to a unitary group of signature (n-1,1), and prove their modularity. The main ingredient of the proof is the calculation of the vertical components appearing in the divisor of a Borcherds product on the integral model.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  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 ...

  2. Kudla--Rapoport cycles and derivatives of local densities

    math.NT 2019-08 conditional novelty 8.0 of 10

    The authors prove the local and global Kudla-Rapoport conjectures and, combining with results of Liu and Garcia-Sankaran, the arithmetic Siegel-Weil formula in arbitrary dimension.

  3. 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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