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KUDLA’S MODULARITY CONJECTURE AND FORMAL FOURIER–JACOBI SERIES

Published online by Cambridge University Press:  01 October 2015

JAN HENDRIK BRUINIER
Affiliation:
Fachbereich Mathematik, Technische Universität Darmstadt, Schlossgartenstraße 7, D-64289 Darmstadt, Germany; bruinier@mathematik.tu-darmstadt.de
MARTIN WESTERHOLT-RAUM
Affiliation:
Chalmers tekniska högskola och Göteborgs Universitet, Institutionen för Matematiska vetenskaper, SE-412 96 Göteborg, Sweden; martin@raum-brothers.eu

Abstract

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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.

Type
Research Article
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s) 2015

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