Rational torsion points of some Jacobians of curves of genus 2. (Points rationnels de torsion de jacobiennes de certaines courbes de genre 2.) (French) Zbl 0783.14016

The author proves
(1) Let \(\ell\) be one of the numbers 21, 22, 23, 25, 26, 27 and 29. Then there exists a curve \(C_ \ell\) of genus 2, the Jacobian of which has a rational torsion point of order \(\ell\). For \(\ell=24\), the author constructs two curves with the same property – which curves are not \(\overline \mathbb{Q}\)-isomorphic (see theorem 1.1).
(2) There exists a family of curves of genus 2 defined over \(\mathbb{Q}\), and depending on one parameter, such that its Jacobian has a subgroup isomorphic to \(\mathbb{Z}/3 \mathbb{Z} \times \mathbb{Z}/9 \mathbb{Z}\) (see theorem 1.2).
Reviewer: A.Iliev (Sofia)


14H40 Jacobians, Prym varieties
14G05 Rational points