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Published online by Cambridge University Press:  01 October 2015

Fachbereich Mathematik, Technische Universität Darmstadt, Schlossgartenstraße 7, D-64289 Darmstadt, Germany;
Chalmers tekniska högskola och Göteborgs Universitet, Institutionen för Matematiska vetenskaper, SE-412 96 Göteborg, Sweden;


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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.

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