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arXiv · 1409.4996

Kudla's Modularity Conjecture and Formal Fourier-Jacobi Series

Jan Hendrik Bruinier·Martin Westerholt-Raum
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Abstract

We prove modularity of formal series of Jacobi forms that satisfy a natural symmetry condition. They are formal analogues of Fourier-Jacobi expansions of Siegel modular forms. From our result and a theorem of Wei Zhang, we deduce Kudla's conjecture on the modularity of generating series of special cycles of arbitrary codimension and for all orthogonal Shimura varieties.

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Jan Hendrik Bruinier, Martin Westerholt-Raum. 2014-09-17. Kudla's Modularity Conjecture and Formal Fourier-Jacobi Series. https://arxiv.org/abs/1409.4996

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