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arXiv · 2310.05637

Constructing $2$-dimensional Lubin-Tate formal groups over $\mathbb{Z}_{p}$ (I)

Ramla Abdellatif·Mabud Ali Sarkar
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Abstract

In this paper, we construct a class of $2$-dimensional formal groups over $\mathbb{Z}_p$ that provide a higher-dimensional analogue of the usual $1$-dimensional Lubin-Tate formal groups, then we initiate the study of the extensions generated by their $p^{n}$-torsion points. For instance, we prove that the coordinates of the $p^{\infty}$-torsion points of such a formal group generate an abelian extension over a certain unramified extension of $\mathbb{Q}_{p}$, and we study some ramification properties of these abelian extensions. In particular, we prove that the extension generated by the coordinates of the $p$-torsion points is in general totally ramified.

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Ramla Abdellatif, Mabud Ali Sarkar. 2023-10-09. Constructing $2$-dimensional Lubin-Tate formal groups over $\mathbb{Z}_{p}$ (I). https://doi.org/10.1016/j.jalgebra.2025.10.027

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