Heights of pre-special points of Shimura varieties

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 Z-Hodge structure. Our bound is the final step needed to complete a proof of the Andre-Oort conjecture under the conjectural lower bounds for the sizes of Galois orbits of special points, using a strategy of Pila and Zannier.

60 pages; added details of correction to Lemma 2.15

References in corpus (3)

• The Andre-Oort conjecture for the moduli space of Abelian Surfaces
• Hyperbolic Ax-Lindemann theorem in the cocompact case
• Categoricity of modular and Shimura curves

Cited by in corpus (2)

• Applications of the hyperbolic Ax-Schanuel conjecture
• Categoricity of modular and Shimura curves