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GALOIS CONJUGATES OF SPECIAL POINTS AND SPECIAL SUBVARIETIES IN SHIMURA VARIETIES

Published online by Cambridge University Press:  30 October 2019

Martin Orr*
Affiliation:
Mathematics Institute, University of Warwick, CoventryCV4 7AL, UK (martin.orr@warwick.ac.uk)

Abstract

Let $S$ be a Shimura variety with reflex field $E$. We prove that the action of $\text{Gal}(\overline{\mathbb{Q}}/E)$ on $S$ maps special points to special points and special subvarieties to special subvarieties. Furthermore, the Galois conjugates of a special point all have the same complexity (as defined in the theory of unlikely intersections). These results follow from Milne and Shih’s construction of canonical models of Shimura varieties, based on a conjecture of Langlands which was proved by Borovoi and Milne.

Type
Research Article
Copyright
© Cambridge University Press 2019

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GALOIS CONJUGATES OF SPECIAL POINTS AND SPECIAL SUBVARIETIES IN SHIMURA VARIETIES
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