Quadratic torsion subgroups of modular Jacobian varieties

Yuan Ren

Quadratic torsion subgroups of modular Jacobian varieties

Number Theory 2020-03-09 v2

Authors: Yuan Ren

Abstract

Let $D$ be an odd square-free positive integer and $C$ a divisor of $D$ . For any quadratic character $\chi$ modulo $C$ , we prove that the $\chi$ -part of the group $J_0(DC)_\text{tor}$ of torsion points of $J_0(DC)$ coincides with the $\chi$ -part of its cuspidal subgroup, away from those primes of bad reduction or where possible congruences between oldforms and newforms occur.

Keywords

modular jacobian varieties quadratic torsion cuspidal subgroup quadratic character bad reduction oldforms newforms

Cite

@article{arxiv.1901.09896,
  title  = {Quadratic torsion subgroups of modular Jacobian varieties},
  author = {Yuan Ren},
  journal= {arXiv preprint arXiv:1901.09896},
  year   = {2020}
}

Comments

arXiv admin note: text overlap with arXiv:1709.02088

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