Rational Torsion on the Generalized Jacobian of a Modular Curve With Cuspidal Modulus
We consider the generalized Jacobian $\widetilde{J}0(N)$ of a modular curve $X0(N)$ with respect to a reduced divisor given by the sum of all cusps on it. When $N$ is a power of a prime $≥ 5$, we exhibit that the group of rational torsion points $\widetilde{J}0(N)(\{Q})Tor$ tends to be much smaller than the classical Jacobian.
2010 Mathematics Subject Classification: Primary 14H40; Secondary 11G16, 11F03, 14G35.
Keywords and Phrases: Generalized Jacobian, torsion points, modular units, cuspidal divisor class.
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