Geodesic
Rational torsion points on Jacobians of modular curves
Hwajong Yoo1
1 Center for Geometry and Physics Institute for Basic Science (IBS) Pohang 37673, Republic of Korea
Acta Arithmetica, Tome 172 (2016) no. 4, pp. 299-304

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Let $p$ be a prime greater than 3. Consider the modular curve $X_0(3p)$ over $\mathbb Q$ and its Jacobian variety $J_0(3p)$ over $\mathbb Q$. Let $\mathcal T(3p)$ and $\mathcal C(3p)$ be the group of rational torsion points on $J_0(3p)$ and the cuspidal group of $J_0(3p)$, respectively. We prove that the $3$-primary subgroups of $\mathcal T(3p)$ and $\mathcal C(3p)$ coincide unless $p\equiv 1 \pmod 9$ and $3^{(p-1)/3} \equiv 1 \pmod {p}$.
DOI : 10.4064/aa8140-12-2015
Keywords: prime greater consider modular curve mathbb its jacobian variety mathbb mathcal mathcal group rational torsion points cuspidal group respectively prove primary subgroups mathcal mathcal coincide unless equiv pmod p equiv pmod

Hwajong Yoo 1

1 Center for Geometry and Physics Institute for Basic Science (IBS) Pohang 37673, Republic of Korea 
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Hwajong Yoo. Rational torsion points on Jacobians of modular curves. Acta Arithmetica, Tome 172 (2016) no. 4, pp. 299-304. doi: 10.4064/aa8140-12-2015

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