Ax-Schanuel for Shimura varieties
成果类型：
Article
署名作者：
Mok, Ngaiming; Pila, Jonathan; Tsimerman, Jacob
刊物名称：
ANNALS OF MATHEMATICS
ISSN/ISSBN：
0003-486X
DOI：
10.4007/annals.2019.189.3.7
发表日期：
2019
页码：
945-978
关键词：
摘要：
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. Our method of proof builds on previous work, combined with a new approach that uses higher-order contact conditions to place varieties yielding intersections of excessive dimension in natural algebraic families.