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

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.

34 pages, research article. This is the second revision. We appreciate comments