Geodesic
Rational torsion points on Jacobians of modular curves
Hwajong Yoo1
1Center 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

DOI

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 
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
@article{10_4064_aa8140_12_2015,
     author = {Hwajong Yoo},
     title = {Rational torsion points on {Jacobians} of modular curves},
     journal = {Acta Arithmetica},
     pages = {299--304},
     year = {2016},
     volume = {172},
     number = {4},
     doi = {10.4064/aa8140-12-2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/aa8140-12-2015/}
}
TY  - JOUR
AU  - Hwajong Yoo
TI  - Rational torsion points on Jacobians of modular curves
JO  - Acta Arithmetica
PY  - 2016
SP  - 299
EP  - 304
VL  - 172
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4064/aa8140-12-2015/
DO  - 10.4064/aa8140-12-2015
LA  - en
ID  - 10_4064_aa8140_12_2015
ER  - 
%0 Journal Article
%A Hwajong Yoo
%T Rational torsion points on Jacobians of modular curves
%J Acta Arithmetica
%D 2016
%P 299-304
%V 172
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4064/aa8140-12-2015/
%R 10.4064/aa8140-12-2015
%G en
%F 10_4064_aa8140_12_2015

Cité par Sources :