Sur certains sous-groupes de torsion de jacobiennes de courbes hyperelliptiques de genreg ≥ 1 |
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| Authors: | Franck Leprévost |
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| Institution: | (1) Département de Mathématiques, CNRS, Equipe d’Arithmétique, Université Paris 7, Tour 45-55; 5ème étage; 2, place Jussieu, F-75252 Paris cedex 05, France;(2) Max-Planck-Institut fur Mathematik, Gottfried-Claren-Str. 26, D-53225 Bonn; Allemagne |
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| Abstract: | We construct a family of hyperelliptic curves of genusg defined over Q whose Jacobians have a rational point of order 2g(2g+1). Forl = 2g
2 + 5g + 5, we construct a family of genusg hyperelliptic curves defined over Q, such that their Jacobians have a rational point of orderl orl / 2 orl / 4. We also construct a hyperelliptic curve of genusg defined over Q, which does not belong to the previous family, and whose Jacobian has a rational point of orderl.
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