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5-TORSION POINTS ON CURVES OF GENUS 2

Published online by Cambridge University Press:  24 August 2001

JOHN BOXALL ,
DAVID GRANT  and
FRANCK LEPRÉVOST
JOHN BOXALL
Affiliation:
Département de Mathématiques et de Mécanique, CNRS – FRE 2271, Universitéde Caen, Esplanade de la Paix, 14032 Caen Cedex, France; [email protected]
DAVID GRANT
Affiliation:
Department of Mathematics, University of Colorado at Boulder, Boulder, CO 80309-0395, USA; [email protected]
FRANCK LEPRÉVOST
Affiliation:
Universitéde Grenoble, Institut Fourier BP 74, F-38402 St-Martin-d'Hères Cedex, France; [email protected]
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Abstract

Let C be a smooth proper curve of genus 2 over an algebraically closed field k. Fix a Weierstrass point ∞in C(k) and identify C with its image in its Jacobian J under the Albanese embedding that uses ∞ as base point. For any integer N[ges ]1, we write JN for the group of points in J(k) of order dividing N and J*N for the subset of JN of points of order N. It follows from the Riemann–Roch theorem that C(k)∩J2 consists of the Weierstrass points of C and that C(k)∩J*3 and C(k)∩J* are empty (see [3]). The purpose of this paper is to study curves C with C(k)∩J*5 non-empty.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 64 , Issue 1 , August 2001 , pp. 29 - 43
Copyright
The London Mathematical Society 2001

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