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KUDLA’S MODULARITY CONJECTURE AND FORMAL FOURIER–JACOBI SERIES

Part of: Cycles and subschemes Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  01 October 2015

JAN HENDRIK BRUINIER  and
MARTIN WESTERHOLT-RAUM
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.

MSC classification

Primary: 11F46: Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms
Secondary: 14C25: Algebraic cycles
Type
Research Article
Information
Forum of Mathematics, Pi , Volume 3 , 2015 , e7
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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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