Heights of pre-special points of Shimura varieties

Christopher Daw, Martin Orr

Research output: Contribution to journalArticlepeer-review

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 André–Oort conjecture under the conjectural lower bounds for the sizes of Galois orbits of special points, using a strategy of Pila and Zannier.
Original languageEnglish
Pages (from-to)1305-1357
JournalMathematische Annalen
DOIs
Publication statusPublished - 11 Nov 2015

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