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Heights of pre-special points of Shimura varieties
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Daw, Christopher and Orr, Martin (2016) Heights of pre-special points of Shimura varieties. Mathematische Annalen, 365 (3-4). pp. 1305-1357. doi:10.1007/s00208-015-1328-3 ISSN 0025-5831.
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Official URL: http://dx.doi.org/10.1007/s00208-015-1328-3
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.
Item Type: | Journal Article | ||||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Journal or Publication Title: | Mathematische Annalen | ||||||||
Publisher: | Springer Verlag | ||||||||
ISSN: | 0025-5831 | ||||||||
Official Date: | August 2016 | ||||||||
Dates: |
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Volume: | 365 | ||||||||
Number: | 3-4 | ||||||||
Page Range: | pp. 1305-1357 | ||||||||
DOI: | 10.1007/s00208-015-1328-3 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Related URLs: | |||||||||
Open Access Version: |
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