Work

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

Year: 2023

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2310.05637

Authors: Abdellatif, Ramla, Sarkar, Mabud Ali

Institutions: Centre National de la Recherche Scientifique, Laboratoire Amiénois de Mathématique Fondamentale et Appliquée, IMAR - Institutul de Matematică „Simion Stoilow” al Academiei Române, Université de Picardie Jules Verne, University of Burdwan

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4387560227

Cites: 9

Cited by:

Related to: 10