$p$-adic hyperbolicity for moduli spaces of abelian motives

Abhishek Oswal, Ananth N. Shankar, Xinwen Zhu +1

We prove that Shimura varieties of abelian type satisfy a $p$-adic Borel-extension property over discretely valued fields. More precisely, let $\mathsf{D}$ denote the rigid-analyti…