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arXiv · 2101.06304

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

Jiacheng Xia
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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.

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Jiacheng Xia. 2021-01-15. Some cases of Kudla's modularity conjecture for unitary Shimura varieties. https://arxiv.org/abs/2101.06304

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