Unlikely intersection in higher-dimensional formal groups

Abstract

In this article, we identify a class of higher-dimensional formal groups over the ring of $p$-adic integers that are uniquely determined by their $p$-power torsion points. More precisely, we prove that if two simple finite-height formal groups share infinitely many torsion points, then they are equal. This extends a rigidity theorem of Berger \cite{LB1} from the one-dimensional setting to a higher-dimensional family of simple formal groups.

15 pages, this is new revised version with several open questions at the end. Comments are welcome!