Vol. 2, No. 2, 2008

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A finiteness property of torsion points

Matthew Baker, Su-ion Ih and Robert Rumely

Vol. 2 (2008), No. 2, 217–248

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

elliptic curve, equidistribution, canonical height, torsion point, integral point
Mathematical Subject Classification 2000
Primary: 11G05
Secondary: 11J71, 11J86, 37F10, 11G50
Received: 29 October 2007
Revised: 11 January 2008
Accepted: 11 January 2008
Published: 15 March 2008
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