Unlikely intersection in higher-dimensional formal groups

Ramla Abdellatif; Mabud Ali Sarkar; Absos Ali Shaikh

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arXiv · 2306.01759

Unlikely intersection in higher-dimensional formal groups

Ramla Abdellatif·Mabud Ali Sarkar·Absos Ali Shaikh

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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.

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Ramla Abdellatif, Mabud Ali Sarkar, Absos Ali Shaikh. 2023-05-25. Unlikely intersection in higher-dimensional formal groups. https://arxiv.org/abs/2306.01759

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