Some cases of Kudla's modularity conjecture for unitary Shimura varieties
Number Theory
2021-02-17 v2 Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.2101.06304,
title = {Some cases of Kudla's modularity conjecture for unitary Shimura varieties},
author = {Jiacheng Xia},
journal= {arXiv preprint arXiv:2101.06304},
year = {2021}
}
Comments
Typos corrected, references added