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Powers of abelian varieties over not isogenous to a Jacobian
Olivier de Gaay Fortman, Ananth N. Shankar
We prove the existence of abelian varieties over with no power isogenous to a Jacobian. Moreover, given a positive integer , we prove the existence of…
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 …
-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…
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 Sh…