KUDLA’S MODULARITY CONJECTURE AND FORMAL FOURIER–JACOBI SERIES

By Jan H. Bruinier, Martin Westerholt-Raum. Forum of Mathematics, Pi, 2014

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We prove modularity of formal series of Jacobi forms that satisfy a natural symmetry condition. They are formal analogs 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.

Subfields: Geometry and Topology, Mathematical Physics

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