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SUMMARY:Torsion Subgroups of Modular Jacobians - Elvira Lupoian (UCL)
DTSTART:20241203T143000Z
DTEND:20241203T153000Z
UID:TALK220102@talks.cam.ac.uk
CONTACT:Jef Laga
DESCRIPTION:In 1977 Mazur proved that the rational torsion subgroup of the
  Jacobian of the modular curve $X_{0}\\left( N \\right)$\, $N \\geq 5$ pri
 me\, is generated by the linear equivalence class of the difference of the
  two cusps. More generally\, it is conjectured that for a general $N$\, th
 e rational torsion subgroup of the Jacobian of $X_{0}\\left( N \\right)$ i
 s generated by cusps. In this talk\, we discuss a generalisation of this t
 o other modular curves\, namely to certain covers of $X_{0}\\left( N \\rig
 ht)$\, indexed by subgroups of $\\left( \\mathbb{Z}/ N \\mathbb{Z} \\right
 )^{*}.
LOCATION:MR13
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