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

2024/04/09 by Jan Hendrik Bruinier, Bruinier, Jan Hendrik, Eugenia Rosu +3 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2404.06254

openalex publication_date 2024/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

Cited by

• The cohomological Kudla conjecture for unitary Shimura varieties

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• Special Cycles on Toroidal Compactifications of Orthogonal Shimura Varieties
• Generating series of intersection volumes of special cycles on unitary Shimura varieties
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