Joint Unlikely Almost Intersections on Ordinary Siegel Spaces

Motivated by the “Mordell–Lang + Bogomolov” (proved by Poonen and independently by S. Zhang), I hope to relax the usual incidence relations in unlikely intersections by using certain distance relations. The focus of this talk is a joint of the conjectures of Andr ́e–Oort and Andr ́e–Pink on a product of ordinary Siegel formal moduli schemes. I will make a conjecture and present partial progress obtained via a perfectoid approach. A closely related analog of the Ax–Lindemann principle will also be discussed. 

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