One-dimensional algebraic formal groups

Robert Coleman

Vol. 122 (1986), No. 1, 35–41

DOI: 10.2140/pjm.1986.122.35

Abstract

Let K be an algebraically closed field of characteristic zero. We shall call an element of K[[x₁,…,x_n]] algebraic if it is algebraic over K(x₁,…,x_n). Thus a one-dimensional algebraic formal group is an element F ∈ K[[x₁,x₂]] such that F is a formal group and F is algebraic. As is well known, such formal groups arise from one-dimensional algebraic groups. Our intention is to show that this is the only way they arise. All formal groups mentioned in this note shall be one-parameter formal groups.

Mathematical Subject Classification 2000

Primary: 14L05

Secondary: 11S31, 14H40

Milestones

Received: 5 December 1983

Published: 1 March 1986