Mathematische Annalen

, Volume 365, Issue 3–4, pp 1305–1357 | Cite as

Heights of pre-special points of Shimura varieties

Article

Abstract

Let s be a special point on a Shimura variety, and x a pre-image of s in a fixed fundamental set of the associated Hermitian symmetric domain. We prove that the height of x is polynomially bounded with respect to the discriminant of the centre of the endomorphism ring of the corresponding \(\mathbb {Z}\)-Hodge structure. Our bound is the final step needed to complete a proof of the André–Oort conjecture under the conjectural lower bounds for the sizes of Galois orbits of special points, using a strategy of Pila and Zannier.

Mathematics Subject Classification

11G18 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Institut des Hautes Études ScientifiquesBures-sur-YvetteFrance
  2. 2.Department of MathematicsImperial College LondonLondonUK

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