Vol. 122, No. 1, 1986

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One-dimensional algebraic formal groups

Robert Coleman

Vol. 122 (1986), No. 1, 35–41
Abstract

Let K be an algebraically closed field of characteristic zero. We shall call an element of K[[x1,,xn]] algebraic if it is algebraic over K(x1,,xn). 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
Authors
Robert Coleman
Department of Mathematics
University of California, Berkeley
Berkeley CA 94720-3840
United States
http://math.berkeley.edu/~coleman/