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Rigidity and unlikely intersections for formal groups

Volume 195 / 2020

Laurent Berger 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


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 $F$.


  • Laurent BergerUMPA de l’ENS de Lyon, UMR 5669 du CNRS
    46 Allée d’Italie
    69007 Lyon, France

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