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Torsion Packets on Curves

Published online by Cambridge University Press:  04 December 2007

Matthew Baker  and
Bjorn Poonen
Matthew Baker
Affiliation:
Department of Mathematics, Harvard University, Cambridge, MA 02138, U.S.A. E-mail: mbaker@math.harvard.edu
Bjorn Poonen
Affiliation:
Department of Mathematics, University of California, Berkeley, CA 94720-3840, U.S.A. E-mail: poonen@math.berkeley.edu
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Abstract

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Let X be a curve of genus g[ges ]2 over a field of characteristic zero. Then X has at most finitely many torsion packets of size greater than 2. Moreover, X has infinitely many torsion packets of size 2 if and only if either g=2, or g=3 and X is both hyperelliptic and bielliptic.

Keywords

torsion pointtorsion packetManin–Mumford conjectureAbelian varietycurveJacobian

Information

Type
Research Article
Information
Compositio Mathematica , Volume 127 , Issue 1 , May 2001 , pp. 109 - 116
Copyright
© 2001 Kluwer Academic Publishers