7 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 …
A characteristic p analogue of the André--Pink--Zannier conjecture
Yeuk Hay Joshua Lam, Ananth N. Shankar
We investigate the analogue of the André--Pink--Zannier conjecture in characteristic . Precisely, we prove it for ordinary function field-valued points with big monodromy, in S…
Abelian varieties not isogenous to Jacobians over global fields
Ananth N. Shankar, Jacob Tsimerman
We prove the existence of abelian varieties not isogenous to Jacobians over characterstic function fields. Our methods involve studying the action of degree Hecke operators…
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…
Canonical Heights on Shimura Varieties and the André-Oort Conjecture
Jonathan Pila, Ananth N. Shankar, Jacob Tsimerman +2
The main purpose of this work is to prove the André-Oort conjecture in full generality.