4 papers · 1 filter
-adic hyperbolicity for Shimura varieties and period images
Benjamin Bakker, Abhishek Oswal, Ananth N. Shankar +1
We prove that Shimura varieties and geometric period images satisfy a -adic extension property for large enough primes . More precisely, let $\mathsf{D}^{\times}\subset \math…
Finiteness of function field-valued points on exceptional Shimura varieties
Benjamin Bakker, Ananth N. Shankar, Jacob Tsimerman
Let be a smooth curve over a finite field of characteristic . We prove that there are finitely many principally polarized abelian schemes of given dimension over …
Integral canonical models of exceptional Shimura varieties
Benjamin Bakker, Ananth N Shankar, Jacob Tsimerman
We prove that Shimura varieties admit integral canonical models for sufficiently large primes. In the case of abelian-type Shimura varieties, this recovers work of Kisin-Kottwitz f…
CM points have everywhere good reduction
Benjamin Bakker, Jacob Tsimerman
We prove that for every Shimura variety , there is an integral model such that all CM points of have good reduction with respect to . In other wor…