Portal de Periódicos da CAPES

KUDLA’S MODULARITY CONJECTURE AND FORMAL FOURIER–JACOBI SERIES

2015; Cambridge University Press; Volume: 3; Linguagem: Inglês

10.1017/fmp.2015.6

2050-5086

Jan Hendrik Bruinier, Martin Raum,

Algebraic structures and combinatorial models

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.