Torsion Subgroups of Modular Jacobians

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• Elvira Lupoian (UCL)
• Tuesday 03 December 2024, 14:30-15:30
• MR13.

If you have a question about this talk, please contact Jef Laga.

In 1977 Mazur proved that the rational torsion subgroup of the Jacobian of the modular curve $X_{0}\left( N \right)$, $N \geq 5$ prime, is generated by the linear equivalence class of the difference of the two cusps. More generally, it is conjectured that for a general $N$, the rational torsion subgroup of the Jacobian of $X_{0}\left( N \right)$ is generated by cusps. In this talk, we discuss a generalisation of this to other modular curves, namely to certain covers of $X_{0}\left( N \right)$, indexed by subgroups of $\left( \mathbb{Z}/ N \mathbb{Z} \right)^{*}.

This talk is part of the Number Theory Seminar series.

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