Rational torsion on the generalized Jacobian of a modular curve with cuspidal modulus
Rational torsion on the generalized Jacobian of a modular curve with cuspidal modulus
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DOI：
10.4171/dm/x11
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发表时间：
2016-06
影响因子：
0.9
通讯作者：
Takao Yamazaki;Yifan Yang
中科院分区：
文献类型：
--
作者：
Takao Yamazaki;Yifan Yang
我们考虑模曲线$X_0(N)$关于其上所有尖点之和给出的约化因子的广义雅可比函数{J}_0(N)$。当$N$是素数$geq 5$的幂时，我们证明了有理扭点群$\widetilde{J}_0(N)(\mathbb{Q})_{\mathrm{Tor}}$往往比经典雅可比小得多。
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.