We prove the Ax-Schanuel theorem for a general (pure) Shimura variety

Mok, Ngaiming

Pila, Jonathan

Tsimerman, Jacob

English

arXiv

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 which uses higher-order contact conditions to place varieties yielding intersections of excessive dimension in natural algebraic families

Mok, N

Tsimerman, J

Oxford University Research Archive

Ax-Schanuel for Shimura varieties

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 which uses higher-order contact conditions to place varieties yielding intersections of excessive dimension in natural algebraic families

Ax-Schanuel for Shimura varieties

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