Let be a Shimura variety with reflex field. We prove that the action of on 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.
|Number of pages||15|
|Journal||Journal of the Institute of Mathematics of Jussieu|
|Early online date||30 Oct 2019|
|Publication status||Published - 1 May 2021|
- Shimura varieties
- canonical models
- special points