Geodesic
Ax-Schanuel for Shimura varieties
Ngaiming Mok1 ; Jonathan Pila2 ; Jacob Tsimerman3
1 The University of Hong Kong, Pokfulam, Hong Kong
2 Mathematical Institute, University of Oxford, Oxford, United Kingdom
3 University of Toronto Toronto, Ontario, Canada
Annals of mathematics, Tome 189 (2019) no. 3, pp. 945-978

Voir la notice de l'article provenant de la source Annals of Mathematics website

We prove the Ax-Schanuel theorem for a general (pure) Shimura variety. A basic version of the theorem concerns the transcendence of the uniformization map from a bounded Hermitian symmetric space to a Shimura variety. We then prove a version of the theorem with derivatives in the setting of jet spaces, and finally a version in the setting of differential fields.

DOI : 10.4007/annals.2019.189.3.7

Ngaiming Mok 1 ; Jonathan Pila 2 ; Jacob Tsimerman 3

1 The University of Hong Kong, Pokfulam, Hong Kong
2 Mathematical Institute, University of Oxford, Oxford, United Kingdom
3 University of Toronto Toronto, Ontario, Canada 
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Ngaiming Mok; Jonathan Pila; Jacob Tsimerman. Ax-Schanuel for Shimura varieties. Annals of mathematics, Tome 189 (2019) no. 3, pp. 945-978. doi: 10.4007/annals.2019.189.3.7

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