Rigidity and unlikely intersections for formal groups
Volume 195 / 2020
Acta Arithmetica 195 (2020), 305-312
MSC: Primary 11S31; Secondary 11F80, 11S82, 13J05, 37P35.
DOI: 10.4064/aa190523-5-12
Published online: 4 May 2020
Abstract
Let $K$ be a $p$-adic field and let $F$ and $G$ be two formal groups over the integers of $K$. We prove that if $F$ and $G$ have infinitely many torsion points in common, then $F=G$. This follows from a rigidity result: any bounded power series that sends infinitely many torsion points of $F$ to torsion points of $F$ is an endomorphism of $F$.
