Some cases of Kudla's modularity conjecture for unitary Shimura varieties

2021/01/15 by Jiacheng Xia, Xia, Jiacheng · 3 citations
Mathematics · #11F27 #11G18 #14G35 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2101.06304

openalex publication_date 2021/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We use the method of Bruinier--Raum to show that symmetric formal Fourier--Jacobi series, in the cases of norm-Euclidean imaginary quadratic fields, are Hermitian modular forms. Consequently, combining a theorem of Yifeng Liu, we deduce Kudla's conjecture on the modularity of generating series of special cycles of arbitrary codimension for unitary Shimura varieties defined in these cases.

Cited by

• On the cohomological dimension of Siegel modular varieties and the modularity of formal Siegel modular forms
• The cohomological Kudla conjecture for unitary Shimura varieties
• On the vanishing order of Jacobi forms at infinity

Related

• Kudla's Modularity Conjecture and Formal Fourier-Jacobi Series
• Kudla's modularity conjecture on integral models of orthogonal Shimura varieties
• Arithmetic special cycles and Jacobi forms
• The cohomological Kudla conjecture for unitary Shimura varieties
• Derived special cycles on Shimura varieties