On torsion points of formal groups over a ring of Witt vectors
type: Item
instance of: scholarly article
title: On torsion points of formal groups over a ring of Witt vectors
zbMATH Open document ID: 0597.14042
DOI: 10.1007/BF01229807
author: Tetsuo Nakamura
published in: Mathematische Zeitschrift
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173795
review text: Let k be a perfect field of characteristic \(p>0\). Let \(W=W(k)\) be the ring of Witt vectors over k and K its quotient field. Let \(\bar{\mathfrak m}\) be the maximal ideal of the ring of integers of an algebraic closure of K. For a one-dimensional formal group F defined over W of finite height h, denote by \(F_{p^ n}\) the set of elements of \(F(\bar{\mathfrak m})\) of order dividing \(p^ n\). Let \(m\geq 1\) and F be a formal group over W of height h, which corresponds to Honda's special element \(p+p^ mc_ 1T+...+p^ mc_{h-1}T^{h-1}+cT^ h\) \((c_ 1,...,c_{h-1},c\in W\), c invertible) [cf. \textit{T. Honda}, J. Math. Soc. Japan 22, 213-246 (1970; Zbl 0202.031)]. In this paper we explicitly describe the Galois extension \(K(F_{p^{m+1}})/K\). We also compute the ramification numbers of the extension. In particular our result gives an explicit description of \(K(F_ p^ 2)/K\) for all formal groups over W of height h.
Mathematics Subject Classification ID: 14L05
Mathematics Subject Classification ID: 12F10
Mathematics Subject Classification ID: 13K05
zbMATH DE Number: 3961839
zbMATH Keywords: torsion points of formal groups
zbMATH Keywords: characteristic p
zbMATH Keywords: ring of Witt vectors
zbMATH Keywords: Honda's special element
zbMATH Keywords: Galois extension
MaRDI profile type: Publication
cites work: Q4067225
cites work: On the theory of commutative formal groups
cites work: Q5612629
cites work: Finite Subgroups of Formal A-Modules over p -Adic Integer Rings
description: scientific article; zbMATH DE number 3961839