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5-Torsion Points on Curves of Genus 2 |
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| Authors: | Boxall, John Grant, David Leprevost, Franck |
| Affiliation: | Département de Mathématiques et de Mécanique, CNRS – FRE 2271, Universitéde Caen Esplanade de la Paix, 14032 Caen Cedex, France, boxall{at}math.unicaen.fr Department of Mathematics, University of Colorado at Boulder Boulder, CO 80309-0395, USA, grant{at}boulder.colorado.edu Universitéde Grenoble Institut Fourier BP 74, F-38402 St-Martin-d'Hères Cedex, France, franck.leprevost{at}ujf-grenoble.fr |
| Abstract: | Let C be a smooth proper curve of genus 2 over an algebraicallyclosed field k. Fix a Weierstrass point  in C(k) and identifyC with its image in its Jacobian J under the Albanese embeddingthat uses as base point. For any integer N 1, we write JN forthe group of points in J(k) of order dividing N and  for the subset of JN of points oforder N. It follows from the RiemannRoch theorem thatC(k) J2 consists of the Weierstrass points of C and that C(k) and C(k) are empty (see [3]). The purpose of this paper is to study curvesC with C(k) non-empty. |
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