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Modularity of special 0-cycles on toroidal compactifications of Shimura Varieties

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arxiv 2404.06254 v1 pith:KCBN62HR submitted 2024-04-09 math.NT

Jan Hendrik Bruinier , Eugenia Rosu , Shaul Zemel This is my paper · ORCID
classification math.NT
keywords cyclesshimuraspecialtoroidalappropriatelychowcompactificationcompactifications
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We consider the generating series of appropriately completed 0-dimensional special cycles on a toroidal compactification of an orthogonal or unitary Shimura variety with values in the Chow group. We prove that it is a holomorphic Siegel, respectively Hermitian, modular form

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Cited by 2 Pith papers

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

  1. Modularity of Higher Theta Series III: Proof of the Modularity Conjecture

    math.NT 2026-08 conditional novelty 8.0 of 10

    The higher theta series on Hermitian shtukas are shown to be modular, independent of the chosen Lagrangian, with a stronger supermodularity result for general linear groups.

  2. The cohomological Kudla conjecture for unitary Shimura varieties

    math.NT 2025-07 conditional novelty 8.0 of 10

    The authors construct explicit boundary corrections making the Kudla-Millson generating series of special cycles on compactified unitary Shimura varieties a holomorphic Hermitian modular form for codimensions g ≤ n/2.

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