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A CHARACTERIZATION OF SPECIAL SUBVARIETIES

Part of:Global differential geometryArithmetic problems. Diophantine geometry

Published online by Cambridge University Press:  07 March 2011

Emmanuel Ullmo and
Andrei Yafaev
Emmanuel Ullmo
Affiliation:
Departement de Mathématique, Université de Paris-Sud, Orsay, France (email: ullmo@math.u-psud.fr)
Andrei Yafaev
Affiliation:
Department of Mathematics, University College London, U.K. (email: yafaev@math.ucl.ac.uk)

Abstract

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We prove that an algebraic subvariety of a Shimura variety is weakly special if and only if analytic components of its preimage in the symmetric space are algebraic. We also prove an analogous result in the case of abelian varieties.

MSC classification

Secondary:14G35: Modular and Shimura varieties14G10: Zeta-functions and related questions (Birch-Swinnerton-Dyer conjecture)53C35: Symmetric spaces

Information

Type
Research Article
Information
Mathematika , Volume 57 , Issue 2 , July 2011, pp. 263 - 273
Copyright
Copyright © University College London 2011

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