Unlikely intersection in higher-dimensional formal groups

2023/05/25 by Mabud Ali Sarkar, Ramla Abdellatif, Sarkar, Mabud Ali +2
Computer Science · Mathematics · #11S31 #13J05 #14K02 #14K05 #Advanced Algebra and Geometry #FOS: Mathematics #Number Theory (math.NT) #Topological and Geometric Data Analysis #advanced mathematical theories #math.NT #msc:11S31 #msc:13J05 #msc:14K02 #msc:14K05

paper · pdf · doi:10.48550/arxiv.2306.01759

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

openalex publication_date 2023/05/25 · openalex created_date 2023/06/07 · openalex updated_date 2026/07/28 · arxiv created 2026/08/03 · arxiv updated 2026/08/04

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 \citeLB1 from the one-dimensional setting to a higher-dimensional family of simple formal groups.

Related

• Rigidity and unlikely intersections for formal groups
• Unlikely intersections on the p-adic formal ball
• Unlikely Intersections in Finite Characteristic
• Constructing 2-dimensional Lubin-Tate formal groups over ℤ_p (I)
• Torsion of algebraic groups and iterate extensions associated with Lubin-Tate formal groups