Rational torsion on the generalized Jacobian of a modular curve with cuspidal modulus
Abstract
We consider the generalized Jacobian $\widetilde{J}_0(N)$ of a modular curve $X_0(N)$ with respect to a reduced divisor given by the sum of all cusps on it. When $N$ is a power of a prime $\geq 5$, we exhibit that the group of rational torsion points $\widetilde{J}_0(N)(\mathbb{Q})_{\mathrm{Tor}}$ tends to be much smaller than the classical Jacobian.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2016
- DOI:
- 10.48550/arXiv.1606.06362
- arXiv:
- arXiv:1606.06362
- Bibcode:
- 2016arXiv160606362Y
- Keywords:
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- Mathematics - Number Theory;
- Mathematics - Algebraic Geometry
- E-Print:
- 17 pages