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The Gross–Kohnen–Zagier theorem over totally real fields

Part of: Arithmetic algebraic geometry Arithmetic problems. Diophantine geometry

Published online by Cambridge University Press:  10 August 2009

Xinyi Yuan ,
Shou-Wu Zhang  and
Wei Zhang
Xinyi Yuan
Affiliation:
Department of Mathematics, Columbia University, New York, NY 10027, USA (email: yxy@math.columbia.edu)
Shou-Wu Zhang
Affiliation:
Department of Mathematics, Columbia University, New York, NY 10027, USA (email: szhang@math.columbia.edu)
Wei Zhang
Affiliation:
Department of Mathematics, Columbia University, New York, NY 10027, USA (email: weizhang@math.columbia.edu)
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Abstract

On Shimura varieties of orthogonal type over totally real fields, we prove a product formula and the modularity of Kudla’s generating series of special cycles in Chow groups.

Keywords

Shimura varieties Kudla cycles Siegel modular forms

MSC classification

Secondary: 11G18: Arithmetic aspects of modular and Shimura varieties 14G35: Modular and Shimura varieties
Type
Research Article
Information
Compositio Mathematica , Volume 145 , Issue 5 , September 2009 , pp. 1147 - 1162
Copyright
Copyright © Foundation Compositio Mathematica 2009

References

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