Vol. 2, No. 2, 2008
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A finiteness property of torsion points

Matthew Baker & Su-ion Ih & Robert Rumely

Vol. 2 (2008), No. 2, 217-248
Abstract

Let k be a number field, and let G be either the multiplicative group Gm ∕ k or an elliptic curve E ∕ k. Let S be a finite set of places of k containing the archimedean places. We prove that if α in G(k) is nontorsion, then there are only finitely many torsion points ξ in G(k)tors that are S-integral with respect to α. We also formulate conjectural generalizations for dynamical systems and for abelian varieties.
Keywords

elliptic curve, equidistribution, canonical height, torsion point, integral point

Mathematical Subject Classification

Primary: 11G05

Secondary: 11J71, 11J86, 37F10, 11G50
Authors
Matthew Baker
School of Mathematics
Georgia Institute of Technology
Atlanta, Georgia 30332-0160
United States
Su-ion Ih
Department of Mathematics
University of Colorado at Boulder
Campus Box 395
Boulder, CO 80309-0395
United States
Robert Rumely
Department of Mathematics
University of Georgia
Athens, Georgia 30602-0002
United States