Galois conjugates of special points and special subvarieties in Shimura varieties

Abstract

Let $S$ be a Shimura variety with reflex field $E$. We prove that the action of $\mathrm{Gal}(\overline{\mathbb{Q}}/E)$ 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.

16 pages

References in corpus (1)

• Applications of the hyperbolic Ax-Schanuel conjecture

Cited by in corpus (1)

• Plectic Galois action on CM points and connected components of Hilbert modular varieties