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Large torsion subgroups of split Jacobians of curves of genus 2. (Sous-groupes de torsion d’ordres élevés de jacobiennes décomposables de courbes de genre 2.) (French) Zbl 0895.11027
The authors present a table of groups \(G\) of orders up to \(128\) which occur as rational torsion subgroups of split Jacobians of curves of genus two over the rational numbers. They also indicate how many of these curves they have found for each of the groups (ranging from one to a two-parameter family). The method of construction is to glue together two elliptic curves with suitable torsion subgroups in a certain way. As an example, some details of the case \(G = \mathbb Z/63\mathbb Z\) are given. A forthcoming paper by the same authors will give a detailed account of the results.

MSC:
11G30 Curves of arbitrary genus or genus \(\ne 1\) over global fields
14H40 Jacobians, Prym varieties
11G10 Abelian varieties of dimension \(> 1\)
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